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All Textbook Solutions for Precalculus
In Problems 3760, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (forexample,y=x2) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function. g(x)=12x3In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. h( x )= x+2In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. h( x )= x+1In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. f( x )= ( x-1 ) 3 +2In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. f( x )= ( x+2 ) 3 -3In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. g( x )=4 xIn Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. g( x )= 1 2 xIn Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. f( x )=- x 3In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. f( x )=- xIn Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. 51. f( x )=2 ( x+1 ) 2 -3In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. 52. f( x )=3 ( x-2 ) 2 +1In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. 53. g( x )=2 x-2 +1In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. 54. g( x )=3| x+1 |-3In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. 55. h( x )= x -2In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. 56. h( x )= 4 x +2In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. 57. f( x )=- ( x+1 ) 3 -1In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. 58. f( x )=-4 x-1In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. 59. g( x )=2| 1-x |In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. 60. g( x )=4 2-x61AYU62AYUIn Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions: a. F( x )=f( x )+3 b. G( x )=f( x+2 ) c. P( x )=-f( x ) d. H( x )=f( x+1 )-2 e. Q( x )= 1 2 f( x ) f. g( x )=-f( x ) g. h( x )=f( 2x ) 63.In Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions: a. F( x )=f( x )+3 b. G( x )=f( x+2 ) c. P( x )=-f( x ) d. H( x )=f( x+1 )-2 e. Q( x )= 1 2 f( x ) f. g( x )=-f( x ) g. h( x )=f( 2x ) 64.In Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions: a. F( x )=f( x )+3 b. G( x )=f( x+2 ) c. P( x )=-f( x ) d. H( x )=f( x+1 )-2 e. Q( x )= 1 2 f( x ) f. g( x )=-f( x ) g. h( x )=f( 2x ) 65.In Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions: a. F( x )=f( x )+3 b. G( x )=f( x+2 ) c. P( x )=-f( x ) d. H( x )=f( x+1 )-2 e. Q( x )= 1 2 f( x ) f. g( x )=-f( x ) g. h( x )=f( 2x ) 66.In Problems 69-76, complete the square of each quadratic expression. Then graph each function using the technique of shifting (If necessary, refer to Appendix A, Section A3 to r eview completing the square.) 69. f( x )= x 2 +2xIn Problems 69-76, complete the square of each quadratic expression. Then graph each function using the technique of shifting (If necessary, refer to Appendix A, Section A3 to r eview completing the square.) 70. f( x )= x 2 6xIn Problems 69-76, complete the square of each quadratic expression. Then graph each function using the technique of shifting (If necessary, refer to Appendix A, Section A3 to r eview completing the square.) 71. f( x )= x 2 8x+1In Problems 69-76, complete the square of each quadratic expression. Then graph each function using the technique of shifting (If necessary, refer to Appendix A, Section A3 to r eview completing the square.) 72. f( x )= x 2 +4x+2In Problems 69-76, complete the square of each quadratic expression. Then graph each function using the technique of shifting (If necessary, refer to Appendix A, Section A3 to r eview completing the square.) 73. f( x )=2 x 2 12x+19In Problems 69-76, complete the square of each quadratic expression. Then graph each function using the technique of shifting (If necessary, refer to Appendix A, Section A3 to r eview completing the square.) 74. f( x )=3 x 2 +6x+1In Problems 69-76, complete the square of each quadratic expression. Then graph each function using the technique of shifting (If necessary, refer to Appendix A, Section A3 to r eview completing the square.) 75. f( x )=3 x 2 12x17In Problems 69-76, complete the square of each quadratic expression. Then graph each function using the technique of shifting (If necessary, refer to Appendix A, Section A3 to r eview completing the square.) 76. f( x )=2 x 2 12x1375AYU76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU90AYU91AYU92AYU93AYU94AYU1. P=( x,y ) be a point on the graph of y= x 2 8 . (a) Express the distance d from P to the origin as a function of x. (b) What is d if x=0 ? (c) What is d if x=1 ? (d) Use a graphing utility to graph d=d( x ) . (e) For what values of x is d smallest?2. P=( x,y ) be a point on the graph of y= x 2 8 . (a) Express the distance d from P to the point ( 0,1 ) as a function of x. (b) What is d if x=0 ? (c) What is d if x=1 ? (d) Use a graphing utility to graph d=d( x ) . (e) For what values of x is d smallest?3. P=( x,y ) be a point on the graph of y= x . (a) Express the distance d from P to the point ( 1,0 ) as a function of x. (b) Use a graphing utility to graph d=d( x ) . (c) For what values of x is d smallest?4. P=( x,y ) be a point on the graph of y= 1 x . (a) Express the distance d from P to the origin as a function of x. (b) Use a graphing utility to graph d=d( x ) . (c) For what values of x is d smallest?5. A right triangle has one vertex on the graph of y= x 3 , x0 , at ( x,y ) , another at the origin, and the third on the positive y-axis at ( 0,y ) , as shown in the figure. Express the area A of the triangle as a function of x.6. A right triangle has one vertex on the graph of y=9 x 2 , x0 , at ( x,y ) , another at the origin, and the third on the positive x-axis at ( x,0 ) . Express the area A of the triangle as a function of x.7. A rectangle has one corner in quadrant I on the graph of y=16 x 2 , another at the origin, a third on the positive y-axis , and the fourth on the positive x-axis . See the figure below. Express the area A of the rectangle as a function of x. What is the domain of A? Graph A=A( x ) . For what value of x is A largest?8. A rectangle is inscribed in a semicircle of radius 2. See the figure. Let P=( x,y ) be the point in quadrant I that is a vertex of the rectangle and is on the circle. (a) Express the area A of the rectangle as a function of x. (b) Express the perimeter p of the rectangle as a function of x. (c) Graph A=A( x ) . For what value of x is A largest? (d) Graph P=P( x ) . For what value of x is p largest?9. A rectangle is inscribed in a semicircle of radius 2. See the figure. Let P=( x,y ) be the point in quadrant I that is a vertex of the rectangle and is on the circle. (a) Express the area A of the rectangle as a function of x. (b) Express the perimeter p of the rectangle as a function of x. (c) Graph A=A( x ) . For what value of x is A largest? (d) Graph P=P( x ) . For what value of x is p largest?10. A circle of radius r is inscribed in a square. see the figure. (a) Express the area A of the square as a function of the radius r of the circle. (b) Express the perimeter p of the square as a function of r.11. Geometry A wire 10 meters long is to be cut into two pieces. One piece will be shaped as a square, and the other piece will be shaped as a circle. See the figure. (a) Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the square. (b) What is the domain of A? (c) Graph A=A( x ) . For what value of x is A smallest?12AYU13. Geometry A wire of length x is bent into the shape of a circle. (a) Express the circumference C of the circle as a function of x. (b) Express the area A of the circle as a function of x.14AYU15. Geometry A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure (a) Express the area A of the rectangle as a function of the radius r of the semicircle. (b) Express the perimeter p of the rectangle as a function of r.16. Geometry An equilateral triangle is inscribed in a circle of radius r. See the figure. Express the circumference C of the circle as a function of the length x of a side of the triangle. [Hint: First show that r 2 = x 2 3 .]17. Geometry An equilateral triangle is inscribed in a circle of radius r. See the figure in Problem 16. Express the area A within the circle, but outside the triangle, as a function of the length x of a side of the triangle.18. Uniform Motion Two cars leave an intersection at the same time. One is headed south at a constant speed of 30 miles per hour, and the other is headed west at a constant speed of 40 miles per hour (see the figure). Build a model that expresses the distance d between the cars as a function of the time t. [Hint: At t=0 , the cars leave the intersection.]19. Uniform Motion Two cars are approaching an intersection. One is 2 miles south of the intersection and is moving at a constant speed of 30 miles per hour. At the same time, the other car is 3 miles east of the intersection and is moving at a constant speed of 40 miles per hour. Build a model that expresses the distance d between the cars as a function of time t. [Hint: At t=0 , the cars are 2 miles south and 3 miles east of the intersection, respectively.] (b) Use a graphing utility to graph d=d( t ) . For what value of t is d smallest?20. Inscribing a Cylinder in a Sphere Inscribe a right circular cylinder of height h and radius r in a sphere of fixed radius R. See the illustration. Express the volume V of the cylinder as a function of h. [Hint: V= r 2 h . Note also the right triangle.]21. Inscribing a Cylinder in a Cone Inscribe a right circular cylinder of height h and radius r in a cone of fixed radius R and fixed height H. see the illustration. Express the volume V of the cylinder as a function of r. [Hint: V= r 2 h . Note the similar triangles.]22. Installing Cable TV MetroMedia Cable is asked to provide service to a customer whose house is located 2 miles from the road along which the cable is buried. The nearest connection box for the cable is located 5 miles down the road. See the figure. (a) If the installation cost is S500 per mile along the road and 700 per mile off the road, build a model that expresses the total cost C of installation as a function of the distance x (in miles) from the connection box to the point where the cable installation turns off the road. Find the domain of C=C( x ) . (b) Compute the cost if x=1 mile. (c) Compute the cost if x=3 miles. (d) Graph the function C=C( x ) . Use TRACE to see how the cost C varies as x changes from 0 to 5. (e) What value of x results in the least cost?23. Time Required to Go from an Island to a Town An island is 2 miles from the nearest point P on a straight shoreline. A town is 12 miles down the shore from P. See the illustration. (a) If a person can row a boat at an average speed of 3 miles per hour and the same person can walk 5 miles per hour, build a model that expresses the time T that it takes to go from the island to town as a function of the distance X from P to where the person lands the boat. (b) What is the domain of Τ? (c) How long will it take to travel from the island to town if the person lands the boat 4 miles from P? (d) How long will it take if the person lands the boat 8 miles from Ρ?24AYU25AYU26AYU1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE1CT2CT3CT5CT4CT6CT7CT8CT9CTFind the distance between the points P=( 1,3 ) and Q=( 4,2 ) . Find the midpoint of the line segment from P to Q .2CRSolve the inequality 5x+30 and graph the solution set.Find the equation of the line containing the points ( 1,4 ) and ( 2,2 ) . Express your answer in slope-intercept form and graph the line.Find the equation of the line perpendicular to the line y=2x+1 and containing the point ( 3,5 ) . Express your answer in slope-intercept form and graph the line.Graph the equation x 2 + y 2 4x+8y5=0 .Does the following relation represent a function? { ( 3,8 ),( 1,3 ),( 2,5 ),( 3,8 ) }For the function f defined by f( x )= x 2 4x+1 , find: a. f( 2 ) b. f( x )+f( 2 ) c. f( x ) d. f( x ) e. f(x+2) f. f( x+h )f( x ) h h0Find the domain of h(z)= 3z1 6z7 .Is the following graph the graph of a function?Consider the function f(x)= x x+4 . a. Is the point (1, 1 4 ) on the graph of f ? b. If x=2 , what is f(x) ? What point is on the graph of f ? c. If f( x )=2 , what is x ? What point is on the graph of f ?Is the function f(x)= x 2 2x+1 even, odd, or neither?Approximate the local maximum values and local minimum values of f( x )= x 2 5x+1 on [4,4] . Determine where the function is increasing and where it is decreasing.If f(x)=3x+5 and g(x)=2x+1 , a. Solve f(x)=g( x ) . b. Solve f(x)g(x) .For the graph of the function f , a. Find the domain and the range of f . b. Find the intercepts. c. Is the graph of f symmetric with respect to the x-axis , the y-axis , or the origin? d. Find f( 2 ) . e. For what value(s) of x is f( x )=3 ? f. Solve f( x )0 . g. Graph y=f( x )+2 . h. Graph y=f(x) . i. Graph y=2f( x ) . j. Is f even, odd, or neither? k. Find the interval(s) on which f is increasing.1AYU2AYU3AYU4AYU5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYUIn Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. f(x)=2x+3In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. g( x )=5x4In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. h( x )=3x+4In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. p(x)=x+6In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. f(x)=x3In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. h( x )=x+4In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. F(x)=4In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. G(x)=2In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.Suppose that f( x )=4x1 and g(x)=2x+5 . a. Solve f( x )=0 . b. Solve f( x )0 . c. Solve f(x)=g( x ) . d. Solve f( x )g(x) . e. Graph y=f( x ) and y=g( x ) and label the point that represents the solution to the equation f( x )=g(x) .Suppose that f( x )=3x+5 and g(x)=2x+15 . a. Solve f( x )=0 . b. Solve f( x )0 . c. Solve f(x)=g( x ) . d. Solve f( x )g(x) . e. Graph y=f( x ) and y=g( x ) and label the point that represents the solution to the equation f( x )=g(x) .In parts (a) - (f), use the following figure. a. Solve f( x )=50 . b Solve f( x )=80 . c. Solve f( x )=0 . d. Solve f( x )50 . c. Solve f( x )80 . f. Solve 0f( x )80 .In parts (a) - (f), use the following figure. a. Solve g( x )=20 . b Solve g( x )=60 . c. Solve g( x )=0 . d. Solve g( x )20 . c. Solve g( x )60 . f. Solve 0g( x )60 .In parts (a) and (b), use the following figure. a. Solve the equation: f( x )=g( x ) . b. Solve the inequality: f( x )g( x ) .In parts (a) and (b), use the following figure. a. Solve the equation: f( x )=g( x ) . b. Solve the inequality: f( x )g( x ) .In parts (a) and (b), use the following figure. a. Solve the equation: f( x )=g( x ) . b. Solve the inequality: g( x )f( x )h( x ) .In parts (a) and (b), use the following figure. a. Solve the equation: f( x )=g( x ) . b. Solve the inequality: g( x )f( x )h( x ) .37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYUWhich of the following functions might have the graph shown? (More than one answer is possible). a. f( x )=2x7 b. g(x)=3x+4 c. H( x )=5 d. F(x)=3x+4 e. G( x )=x+2Which of the following functions might have the graph shown? More than one answer is possible). a. f( x )=3x+1 b. g( x )=2x+3 c. H( x )=3 d. F( x )=4x1 e. G(x)= 2 3 x+3Under what circumstances is a linear function f( x )=mx+b odd? Can a linear function ever be even?Explain how the graph of f( x )=mx+b can be used to solve mx+b0 .Plot the points ( 1,5 ),( 2,6 ),( 3,9 ),( 1,12 ) in the Cartesian plane. Is the relation { ( 1,5 ),( 2,6 ),( 3,9 ),( 1,12 ) } a function? Why? (pp. 2 and 57-60)Find an equation of the line containing the points ( 1,4 ) and ( 3,8 ) . (pp. 35-36)A _____________ is used to help us to see what type of relation, if any, may exist between two variables.True or False The correlation coefficient is a measure of the strength of a linear relation between two variables and must lie between 1 and 1, inclusive.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.Candy The following data represent the weight (in grams) of various candy bars and the corresponding number of calories. (a) Draw a scatter diagram of the data, treating weight as the independent variable. (b) What type of relation appears to exist between the weight of a candy bar and the number of calories? (c) Select two points and find a linear model that contains the points. (d) Graph the line on the scatter diagram drawn in part (a). (e) Use the linear model to predict the number of calories in a candy bar that weighs 62.3 grams. (f) Interpret the slope of the line found in part (c).Tornadoes The following data represent the width (in yards) and length (in miles) of tornadoes. (a) Draw a scatter diagram of the data, treating width as the independent variable. (b) What type of relation appears to exist between the width and the length of tornadoes? (c) Select two points and find a linear model that contains the points. (d) Graph the line on the scatter diagram drawn in part (b). (e) Use the linear model to predict the length of a tornado that has a width of 450 yards. (f) Interpret the slope of the line found in part (c).Video Games and Grade-Point Average Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week. h , to the cumulative grade-point average. G , of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the students cumulative grade-point average. (a) Explain why the number of hours spent playing video games is the independent variable and cumulative grade-point average is the dependent variable. (b) Use a graphing utility to draw a scatter diagram. (c) Use a graphing utility to find the line of best fit that models the relation between number of hours of video game playing each week and grade-point average. Express the model using function notation. (d) Interpret the slope. (e) Predict the grade-point average of a student who plays video games for 8 hours each week. (f) How many hours of video game playing do you think a student plays whose grade-point average is 2.40 ?20AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYUList the intercepts of the equation y= x 2 9 . (pp. 18-19)2AYUTo complete the square of x 2 5x , you add the number ______. (p. A49)To graph y= (x4) 2 you shift the graph of y= x 2 to the _______ a distance of ________ units. (pp. 106-108)The graph of a quadratic function is called a(n) ____________.The vertical line passing through the vertex of a parabola is called the ________________.The x-coordinate of the vertex of f( x )=a x 2 +bx+c,a0 , is ______.True or False The graph of f( x )=2 x 2 +3x4 opens up.True or False The y-coordinate of the vertex of f( x )= x 2 +4x+5 is f( 2 ) .True or False If the discriminant b 2 4ac=0 , the graph of f( x )=a x 2 +bx+c,a0 , will touch the x-axis at its vertex.In Problems 13-20, match each graph to one the following functions. f( x )= x 2 1In Problems 13-20, match each graph to one the following functions. f(x)= x 2 1In Problems 13-20, match each graph to one the following functions. f(x)= x 2 2x+1In Problems 13-20, match each graph to one the following functions. f( x )= x 2 +2x+1In Problems 13-20, match each graph to one the following functions. f( x )= x 2 2x+2In Problems 13-20, match each graph to one the following functions. f( x )= x 2 +2xIn Problems 13-20, match each graph to one the following functions. f( x )= x 2 2xIn Problems 13-20, match each graph to one the following functions. f( x )= x 2 +2x+2In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )= 1 4 x 2In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )=2 x 2 +4In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f(x)= (x+2) 2 2In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )= (x3) 2 10In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f(x)= x 2 +4x+2In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )= x 2 6x1In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )=2 x 2 4x+1In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f(x)=3 x 2 +6xIn Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f(x)= x 2 2xIn Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )=2 x 2 +6x+2In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )= x 2 +x1In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f(x)=2/3 x 2 +4/3x1In Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )= x 2 +2xIn Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f(x)= x 2 4xIn Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )= x 2 6xIn Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f(x)= x 2 +4xIn Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f(x)= x 2 +2x8In Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )= x 2 2x3In Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )= x 2 +2x+1In Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )= x 2 +6x+9In Problems 33-48, (a) graph each quadratic function by determining whether Us graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )=2 x 2 x+2In Problems 33-48, (a) graph each quadratic function by determining whether Us graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )=4 x 2 2x+1In Problems 33-48, (a) graph each quadratic function by determining whether Us graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )=2 x 2 +2x3In Problems 33-48, (a) graph each quadratic function by determining whether Us graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f(x)=3 x 2 +3x2In Problems 33-48, (a) graph each quadratic function by determining whether Us graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )=3 x 2 +6x+2In Problems 33-48, (a) graph each quadratic function by determining whether Us graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )=2 x 2 +5x+3In Problems 33-48, (a) graph each quadratic function by determining whether Us graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f(x)=4 x 2 6x+2In Problems 33-48, (a) graph each quadratic function by determining whether Us graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f(x)=3 x 2 8x+2In Problems 49-54, determine the quadratic function whose graph is given.In Problems 49-54, determine the quadratic function whose graph is given.In Problems 49-54, determine the quadratic function whose graph is given.In Problems 49-54, determine the quadratic function whose graph is given.In Problems 49-54, determine the quadratic function whose graph is given.In Problems 49-54, determine the quadratic function whose graph is given.In Problems 6572, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value, and then find the value. f(x)=3x2+24xIn Problems 55-62, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value. f( x )=2 x 2 +12xIn Problems 55-62, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value. f( x )=2 x 2 +12x3In Problems 55-62, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value. f( x )=4 x 2 8x+3In Problems, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value, and then find the value.
In Problems 55-62, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value. f(x)=2 x 2 +8x+3In Problems, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value, and then find the value.
In Problems 55-62, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value. f( x )=4 x 2 4xThe graph of the function f( x )=a x 2 +bx+c has vertex at ( 0,2 ) and passes through the point ( 1,8 ) . Find a,b,andc .The graph of the function f(x)=a x 2 +bx+c has vertex at ( 1,4 ) and passes through the point (1,8) . Find a,b,andc .In Problems 77-82, for the given functions fandg , (a) Graph fandg on the same Cartesian plane. (b) Solve f( x )=g( x ) . (c) Use the result of part (b) to label the points of intersection of the graphs of fandg . Shade the region for which f( x )g( x ) , that is, the region below f and above g . f( x )=2x1;g(x)= x 2 4In Problems 77-82, for the given functions fandg , (a) Graph fandg on the same Cartesian plane. (b) Solve f( x )=g( x ) . (c) Use the result of part (b) to label the points of intersection of the graphs of fandg . Shade the region for which f( x )g( x ) , that is, the region below f and above g . f(x)=2x1;g(x)= x 2 9In Problems 77-82, for the given functions fandg , (a) Graph fandg on the same Cartesian plane. (b) Solve f( x )=g( x ) . (c) Use the result of part (b) to label the points of intersection of the graphs of fandg . Shade the region for which f( x )g( x ) , that is, the region below f and above g . f( x )= x 2 +4;g( x )=2x+1In Problems 77-82, for the given functions fandg , (a) Graph fandg on the same Cartesian plane. (b) Solve f( x )=g( x ) . (c) Use the result of part (b) to label the points of intersection of the graphs of fandg . Shade the region for which f( x )g( x ) , that is, the region below f and above g . f( x )= x 2 +9;g( x )=2x+1In Problems 77-82, for the given functions fandg , (a) Graph fandg on the same Cartesian plane. (b) Solve f( x )=g( x ) . (c) Use the result of part (b) to label the points of intersection of the graphs of fandg . Shade the region for which f( x )g( x ) , that is, the region below f and above g . f( x )= x 2 +5x;g(x)= x 2 +3x4