Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus Enhanced with Graphing Utilities
True or False The equation 3x+4y=6 is written in general form.True or False The slope of the line 2y=3x+5 is 3.True or False The point ( 1,2 ) is on the line 2x+y=4 .7AYU8AYU9AYU10AYUIn Problems 13-16, (a) find the slope of the line and (b) interpret the slope.In Problems 13-16, (a) find the slope of the line and (b) interpret the slope.In Problems 13-16, (a) find the slope of the line and (b) interpret the slope.In Problems 13-16, (a) find the slope of the line and (b) interpret the slope.In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (2,3);(4,0)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (4,2);(3,4)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (2,3);(2,1)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (1,1);(2,3)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (3,1);(2,1)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (4,2);(5,2)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (1,2);(1,2)In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. (2,0);(2,2)In Problems 25-32, graph the line containing the point P and having slope m . P=( 1,2 );m=3In Problems 25-32, graph the line containing the point P and having slope m . P=( 2,1 );m=4In Problems 25-32, graph the line containing the point P and having slope m . P=( 2,4 );m= 3 4In Problems 25-32, graph the line containing the point P and having slope m . P=( 1,3 );m= 2 5In Problems 25-32, graph the line containing the point P and having slope m . P=( 1,3 );m=0In Problems 25-32, graph the line containing the point P and having slope m . P=( 2,4 );m=0In Problems 25-32, graph the line containing the point P and having slope m . P=( 0,3 ) ; slope undefinedIn Problems 25-32, graph the line containing the point P and having slope m . P=(2,0) ; slope undefinedIn Problems 33-38, the slope and a point on a line are given. Use this information to locate three additional points on the line Answers may vary. [Hint: It is not necessary to find the equation of the line. See Example 2.] Slope 4; point ( 1,2 )In Problems 33-38, the slope and a point on a line are given. Use this information to locate three additional points on the line Answers may vary. [Hint: It is not necessary to find the equation of the line. See Example 2.] Slope 2; point ( 2,3 )In Problems 33-38, the slope and a point on a line are given. Use this information to locate three additional points on the line Answers may vary. [Hint: It is not necessary to find the equation of the line. See Example 2.] Slope 3 2 ; point ( 2,4 )In Problems 33-38, the slope and a point on a line are given. Use this information to locate three additional points on the line Answers may vary. [Hint: It is not necessary to find the equation of the line. See Example 2.] Slope 4 3 ; point ( 3,2 )In Problems 33-38, the slope and a point on a line are given. Use this information to locate three additional points on the line Answers may vary. [Hint: It is not necessary to find the equation of the line. See Example 2.] Slope 2 ; point ( 2,3 )In Problems 33-38, the slope and a point on a line are given. Use this information to locate three additional points on the line Answers may vary. [Hint: It is not necessary to find the equation of the line. See Example 2.] Slope 1 ; point ( 4,1 )In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 39-46, find an equation of the line L .In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope =3 ; containing the point ( 2,3 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope =2 ; containing the point ( 4,3 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope = 2 3 ; containing the point ( 1,1 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope = 1 2 ; containing the point ( 3,1 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope =3 ; y-intercept=3In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope =5 ; y-intercept=7In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Containing the points ( 1,3 )and( 1,2 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Containing the points ( 3,4 )and( 2,5 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. x-intercept=2;y-intercept=1In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. x-intercept=4;y-intercept=4In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope undefined; containing the point ( 2,4 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Slope undefined; containing the point ( 3,8 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Horizontal; containing the point ( 3,2 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Vertical; containing the point ( 4,5 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line y=4x ; containing the point ( 1,2 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line y=3x ; containing the point (1,2)In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line 5xy=2 ; containing the point ( 0,0 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line x2y=5 ; containing the point ( 0,0 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line x=5 ; containing the point ( 4,2 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Parallel to the line y=5 ; containing the point ( 4,2 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line y= 1 6 x+4 ; containing the point (1,6)In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line y=8x3 ; containing the point (10,2)In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line 2x+5y=2 ; containing the point ( 3,6 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line x3y=12 ; containing the point ( 0,4 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line x=8 ; containing the point ( 3,4 )In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Perpendicular to the line y=8 ; containing the point ( 3,4 )In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. y=2x+3In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. y=3x+4In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. 1 4 y=x1In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. 1 3 x+y=2In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. y= 1 2 x+2In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. y=2x+ 1 2In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. x+4y=4In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. x+3y=6In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. 2x3y=6In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. 3x+2y=6In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. x+y=1In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. xy=2In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. x=4In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. y=1In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. y=5In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. x=2In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. yx=0In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. x+y=0In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. 2y3x=0In Problems 73-92, find the slope and y-intercept of each line. Graph the line by hand. Verify your graph using a graphing utility. 3x+2y=0In Problems 93—102, (a) find the intercepts of the graph of each equation and (b) graph the equation. 2x+3y=6In Problems 93—102, (a) find the intercepts of the graph of each equation and (b) graph the equation. 3x2y=6In Problems 93—102, (a) find the intercepts of the graph of each equation and (b) graph the equation. 4x+5y=40In Problems 93—102, (a) find the intercepts of the graph of each equation and (b) graph the equation. 6x4y=24In Problems 93—102, (a) find the intercepts of the graph of each equation and (b) graph the equation. 7x+2y=21In Problems 93—102, (a) find the intercepts of the graph of each equation and (b) graph the equation. 5x+3y=18In Problems 93—102, (a) find the intercepts of the graph of each equation and (b) graph the equation. 1 2 x+ 1 3 y=1In Problems 93—102, (a) find the intercepts of the graph of each equation and (b) graph the equation. x 2 3 y=4In Problems 93—102, (a) find the intercepts of the graph of each equation and (b) graph the equation. 0.2x0.5y=1In Problems 93—102, (a) find the intercepts of the graph of each equation and (b) graph the equation. 0.3x+0.4y=1.2Find an equation of the x-axis .Find an equation of the y-axis .In Problems 105-108, the equations of two lines are given. Determine whether the lines are parallel, perpendicular, or neither. y=2x3 y=2x+4In Problems 105-108, the equations of two lines are given. Determine whether the lines are parallel, perpendicular, or neither. y= 1 2 x3 y=2x+4In Problems 105-108, the equations of two lines are given. Determine whether the lines are parallel, perpendicular, or neither. y=4x+5 y=4x+2In Problems 105-108, the equations of two lines are given. Determine whether the lines are parallel, perpendicular, or neither. y=2x+3 y= 1 2 x+2In Problems 109-112, write an equation of each line. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.In Problems 109-112, write an equation of each line. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.In Problems 109-112, write an equation of each line. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.In Problems 109-112, write an equation of each line. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.Geometry Use slopes to show that the triangle whose vertices are ( 2,5 ),( 1,3 ),and( 1,0 ) is a right triangle.Geometry Use slopes to show that the quadrilateral whose vertices are ( 1,1 ),( 4,1 ),( 2,2 )and( 5,4 ) is a parallelogram.Geometry Use slopes to show that the quadrilateral whose vertices are ( 1,0 ),( 2,3 ),( 1,2 ),and( 4,1 ) is a rectangle.Geometry Use slopes and the distance formula to show that the quadrilateral whose vertices are ( 0,0 ),( 1,3 ),( 4,2 ),and( 3,1 ) is a square.Geometry Truck Rentals A truck rental company rents a moving truck for one day by charging 39 plus 0.60 per mile. Write a linear equation that relates the cost C , in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 110 miles? 230 miles?Cost Equation The fixed costs of operating a business are the costs incurred regardless of the level of production. Fixed costs include rent, fixed salaries, and costs of leasing machinery. The variable costs of operating a business are the costs that change with the level of output. Variable costs include raw materials, hourly wages,and electricity. Suppose that a manufacturer of jeans has fixed daily costs of $500 and variable costs of 8 for each pair of jeans manufactured. Write a linear equation that relates the daily cost C . in dollars, of manufacturing the jeans to the number x of jeans manufactured. What is the cost of manufacturing 400 pairs of jeans? 740 pairs?Cost of Driving a Car The annual fixed costs far owning a small sedan are 1461 , assuming the car is completely paid for. The cost to drive the car is approximately 0.16 per mile. Write a linear equation that relates the cost C and the number x of miles driven annually. Source: AAA, 2014Wages of a Car Salesperson Dan receives 375 per week for selling new and used cars at a car dealership in Oak Lawn, Illinois. In addition, he receives 5 of the profit on any sales that he generates. Write a linear equation that represents Dan’s weekly salary S when he has sales that generate a profit of x dollars.Electricity Rates in Illinois Commonwealth Edison Company supplies electricity to residential customers for a monthly customer charge of 15.14 plus 7.57 cents per kilowatt- hour for up to 800 kilowatt-hours (kW h). (a) Write a linear equation that relates the monthly charge C in dollars, to the number x of kilowatt-hours used in a month, 0x800 . (b) Graph this equation. (c) What is the monthly charge for using 200 kilowatt-hours? (d) What is the monthly charge for using 500 kilowatt-hours? (e) Interpret the slope of the line. Source: Commonwealth Edison Company, January 2015.Electricity Rates in Florida Florida Power 7.57 plus 9.01 cents per kilowatt-hour for up to 1000 kilowatt-hours. (a) Write a linear equation that relates the monthly charge C , in dollars, to the number x of kilowatt-hours used in a month, 0x1000 . (b) Graph this equation. (c) What is the monthly charge for using 200 kilowatt-hours? (d) What is the monthly charge for using 500 kilowatt-hours? (e) Interpret the slope of the line. Source: Florida Power & Light Company, March 2015.Electricity Rates in Florida Measuring Temperature The relationship between Celsius ( C ) and Fahrenheit ( F ) degrees of measuring temperature is linear. Find a linear equation relating CandF if 0C corresponds to 32Fand100C corresponds to 212F . Use the equation to find the Celsius measure of 70F .Measuring Temperature The Kelvin (K) scale for measuring temperature is obtained by adding 273 to the Celsius temperature. (a) Write a linear equation relating KandC . (b) Write a linear equation relating KandF (see Problem 123).Access Ramp A wooden access ramp is being built to reach a platform that sits 30 inches above the floor. The ramp drops 2 inches for every 25-inch run.Cigarette Use A report in the Child Trends DataBase indicated that, in 2000, 20.6 of twelfth grade students reported daily use of cigarettes. In 2013, 8.5 of twelfth grade students reported daily use of cigarettes. (a) Write a linear equation that relates the percent y of twelfth grade students who smoke cigarettes daily to the number x of years after 2000. (b) Find the intercepts of the graph of your equation. (c) Do the intercepts have any meaningful interpretation? (d) Use your equation to predict the percent for the year 2025. Is this result reasonable? Source:www.childtrends.orgProduct Promotion A cereal company finds that the number of people who will buy one of its products in the first month that the product is introduced is linearly related to the amount of money it spends on advertising. If it spends 40,000 on advertising, then 100,000 boxes of cereal will be sold, and if it spends 60,000 , then 200,000 boxes will be sold. (a) Write a linear equation that relates the amount A spent on advertising to the number x of boxes the company aims to sell. (b) How much expenditure on advertising is needed to sell 300,000 boxes of cereal? (c) Interpret the slope.Show that the line containing the points ( a,b )and( b,a ),ab , is perpendicular to the line y=x . Also show that the midpoint of (a,b)and( b,a ) lies on the line y=x .The equation 2xy=C defines a family of lines, one line for each value of C . On one set of coordinate axes, graph the members of the family when C=4,C=0,andC=2 . Can you draw a conclusion from the graph about each member of the family?Prove that if two nonvertical lines have slopes whose product is -1, then the lines are perpendicular. [Hint: Refer to Figure 65 and use the converse of the Pythagorean Theorem.]Which of the following equations might have the graph shown? (More than one answer is possible.) (a) 2x+3y=6 (b) 2x+3y=6 (c) 3x4y=12 (d) xy=1 (e) xy=1 (f) y=3x5 (g) y=2x+3 (h) y=3x+3Which of the following equations might have the graph shown? (More than one answer is possible.) (a) 2x+3y=6 (b) 2x3y=6 (c) 3x+4y=12 (d) xy=1 (e) xy=1 (f) y=2x1 (g) y= 1 2 x+10 (h) y=x+4The figure shows the graph of two parallel lines. Which of the following pairs of equations might have such a graph? (a) x2y=3 x+2y=7 (b) x+y=2 x+y=1 (c) xy=2 xy=1 (d) xy=2 2x2y=4 (e) x+2y=2 x+2y=1The figure shows the graph of two perpendicular lines. Which of the following pairs of equations might have such a graph? (a) y2x=2 y+2x=1 (b) y2x=0 2y+x=0 (c) 2yx=2 2y+x=2 (d) y2x=2 x+2y=1 (e) 2x+y=2 2y+x=2m is for Slope The accepted symbol used to denote the slope of a line is the letter m. Investigate the origin of this symbolism. Begin by consulting a French dictionary and looking up the French word monter. Write a brief essay on your findings.Grade of a Road The term grade is used to describe the inclination of a road. How is this term related to the notion of slope of a line? Is a 4 grade very steep? Investigate the grades of some mountainous roads and determine their slopes. Write a brief essay on your findings.Carpentry Carpenters use the term pitch to describe the steepness of staircases and roofs. How is pitch related to slope? Investigate typical pitches used for stairs and for roofs. Write a brief essay on your findings.Can the equation of every line be written in slope-intercept form? Why?Does every line have exactly one x-intercept and one y-intercept ? Are there any lines that have no intercepts?What can you say about two lines that have equal slopes and equal y-intercept ?What can you say about two lines with the same x-intercept and the same y-intercept ? Assume that the x-intercept is not 0.If two distinct lines have the same slope but different x-intercept , can they have the same y-intercept ?If two distinct lines have the same y-intercept but different slopes, can they have the same x-intercept ?Which form of the equation of a line do you prefer to use? Justify your position with an example that shows that your choice is better than another. Have reasons.What Went Wrong? A student is asked to find the slope of the line joining (3,2)and(1,4) . He states that the slope is 3 2 . Is he correct? If not, what went wrong?144AYUIn Problems 1-4, find the following for each pair of points: a. The distance between the points. b. The midpoint of the line segment connecting the points. c. The slope of the line containing the points. d. Then interpret the slope found in part (c). 1. ( 0,0 );( 4,2 )In Problems 1-4, find the following for each pair of points: a. The distance between the points. b. The midpoint of the line segment connecting the points. c. The slope of the line containing the points. d. Then interpret the slope found in part (c). 2. (1,1);(2,3)In Problems 1-4, find the following for each pair of points: a. The distance between the points. b. The midpoint of the line segment connecting the points. c. The slope of the line containing the points. d. Then interpret the slope found in part (c). 3. (4,4);(4,8)In Problems 1-4, find the following for each pair of points: a. The distance between the points. b. The midpoint of the line segment connecting the points. c. The slope of the line containing the points. d. Then interpret the slope found in part (c). 4. (2,1);(3,1)5. List the intercepts of the following graph.6. Graph y= x 2 +15 using a graphing utility. Create a table of values to determine a good initial viewing window. Use a graphing utility to approximate the intercepts.7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYU19AYU20AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYUIn Problems 37-44, find the standard form of the equation of each circle. 43. Center (1,3) and tangent to the line y=2 .In Problems 37-44, find the standard form of the equation of each circle. 44. Center ( 4,2 ) and tangent to the line x=1 .In Problems 45-48, match each graph with the correct equation. 45. a. ( x3 ) 2 + ( y+3 ) 2 =9 b. ( x+1 ) 2 + ( y2 ) 2 =4 c. ( x1 ) 2 + ( y+2 ) 2 =4 d. ( x+3 ) 2 + ( y3 ) 2 =9In Problems 45-48, match each graph with the correct equation. 46. a. ( x3 ) 2 + ( y+3 ) 2 =9 b. ( x+1 ) 2 + ( y2 ) 2 =4 c. ( x1 ) 2 + ( y+2 ) 2 =4 d. ( x+3 ) 2 + ( y3 ) 2 =9In Problems 45-48, match each graph with the correct equation. 47. a. ( x3 ) 2 + ( y+3 ) 2 =9 b. ( x+1 ) 2 + ( y2 ) 2 =4 c. ( x1 ) 2 + ( y+2 ) 2 =4 d. ( x+3 ) 2 + ( y3 ) 2 =9In Problems 45-48, match each graph with the correct equation. 48. a. ( x3 ) 2 + ( y+3 ) 2 =9 b. ( x+1 ) 2 + ( y2 ) 2 =4 c. ( x1 ) 2 + ( y+2 ) 2 =4 d. ( x+3 ) 2 + ( y3 ) 2 =949. Find the area of the square in the figure.50. Find the area of the blue shaded region in the figure, assuming the quadrilateral inside the circle is a square.51AYU52AYU53AYU54. The tangent line to a circle may be defined as the line that intersects the circle in a single point, called the point of tangency. See the figure. If the equation of the circle is x 2 + y 2 = r 2 and the equation of the tangent line is y=mx+b , show that: a. r 2 ( 1+ m 2 )= b 2 [Hint: The quadratic equation x 2 + ( mx+b ) 2 = r 2 has exactly one solution.] b. The point of tangency is ( r 2 m b , r 2 b ) . c. The tangent line is perpendicular to the line containing the center of the circle and the point of tangency55. The Greek Method the Greek method for finding the equation of the tangent line to a circle uses the fact that at any point on a circle the lines containing the center and the tangent line are perpendicular (see Problem 54). Use this method to find an equation of the tangent line to the circle x 2 + y 2 =9 at the point ( 1,2 2 ) .56. Use the Greek method described in Problem 55 to find an equation of the tangent line to the circle x 2 + y 2 4x+6y+4=0 at the point ( 3,2 2 3 ) .57. Refer to Problem 54. The line x2y+4=0 is tangent to a circle at ( 0,2 ) . The line y=2x7 is tangent to the same circle at (3,1) . Find the center of the circle.58. Find an equation of the line containing the centers of the two circles x 2 + y 2 4x+6y+4=0 and x 2 + y 2 +6x+4y+9=0 .59AYU60. If the circumference of a circle is 6 , what is its radius?61. Which of the following equations might have the graph shown? (More than one answer is possible.) a. (x2) 2 + (y+3) 2 =13 b. (x2) 2 + (y2) 2 =8 c. (x2) 2 + (y3) 2 =13 d. (x+2) 2 + (y2) 2 =8 e. x 2 + y 2 4x9y=0 f. x 2 + y 2 +4x2y=0 g. x 2 + y 2 9x4y=0 h. x 2 + y 2 4x4y=462. Which of the following equations might have the graph shown? (More than one answer is possible.) a. (x2) 2 + y 2 =3 b. (x+2) 2 + y 2 =3 c. x 2 + (y2) 2 =3 d. (x+2) 2 + y 2 =4 e. x 2 + y 2 +10x+16=0 f. x 2 + y 2 +10x2y=1 g. x 2 + y 2 +9x+10=0 h. x 2 + y 2 9x10=063. Explain how the center and radius of a circle can be used to graph the circle.64AYUIn Problems 1 and 2, determine whether each relation represents a function. For each function, state the domain and range. { ( 1,0 ),( 2,3 ),( 4,0 ) }2REIn Problems 3-5, find the following for each function. (a) f( 2 ) (b) f( 2 ) (c) f( x ) (d) f( x ) (e) f( x2 ) (f) f( 2x ) f( x )= 3x x 2 1In Problems 3-5, find the following for each function. (a) f( 2 ) (b) f( 2 ) (c) f( x ) (d) f( x ) (e) f( x2 ) (f) f( 2x ) f( x )= x 2 4In Problems 3-5, find the following for each function. (a) f( 2 ) (b) f( 2 ) (c) f( x ) (d) f( x ) (e) f( x2 ) (f) f( 2x ) f( x )= x 2 4 x 2In Problems 6-11, find the domain of each function. f( x )= x x 2 9In Problems 6-11, find the domain of each function. f( x )= 2xIn Problems 6-11, find the domain of each function. g( x )= | x | xIn Problems 6-11, find the domain of each function. f( x )= x x 2 +2x3In Problems 6-11, find the domain of each function. f( x )= x+1 x 2 4In Problems 6-11, find the domain of each function. g( x )= x x+8In Problems 12-14, find f+g,fg,fg,and f g for each pair of functions. State the domain of each of these functions. f( x )=2x;g( x )=3x+113RE14REFind the difference quotient of f( x )=2 x 2 +x+1 ; that is, find f( x+h )f( x ) h ,h0 .Consider the graph of the function f on the right. (a) Find the domain and the range of f . (b) List the intercepts. (c) Find f( 2 ) . (d) For what value of x does f( x )=3 ? (e) Solve f( x )0 . (f) Graph y=f( x3 ) . (g) Graph y=f( 1 2 x ) . (h) Graph y=f( x ) .Use the graph of the function f shown to find: (a) The domain and the range of f . (b) The intervals on which f is increasing, decreasing, or constant. (c) The local minimum values and local maximum values. (d) The absolute maximum and absolute minimum. (e) Whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin. (f) Whether the function is even, odd, or neither. (g) The intercepts, if any.In Problems 18-21, determine (algebraically) whether the given function is even, odd, or neither. f( x )= x 3 4x19RE20RE21REIn Problems 22 and 23, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. f( x )=2 x 3 5x+1[ 3,3 ]In Problems 22 and 23, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. f( x )=2 x 4 5 x 3 +2x+1[ 2,3 ]Find the average rate of change of f( x )=8 x 2 x : (a) From 1 to 2 (b) From 0 to 1 (c) From 2 to 425RE26REIn Problems 27 and 28, is the graph shown the graph of a function?In Problems 27 and 28, is the graph shown the graph of a function?In Problems 29 and 30, graph each function. Be sure to label at least three points. f( x )=| x |In Problems 29 and 30, graph each function. Be sure to label at least three points. f( x )=| x |In Problems 31-36, graph each function using the techniques of shifting, compressing or stretching, anti reflections. Identify any intercepts of the graph, State the domain and, based on the graph, find the range. F( x )=| x |4In Problems 31-36, graph each function using the techniques of shifting, compressing or stretching, anti reflections. Identify any intercepts of the graph, State the domain and, based on the graph, find the range. g( x )=2| x |33RE34RE35RE36REIn Problems 37 and 38: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. f( x )={ 3xif2x1 x+1ifx138REA function f is defined by f( x )= Ax+5 6x2 If f( x )=4 , find A .40RE41RE1CT2CT3CT4CT5CT6CT7CT8CTIn Problems 1-6, find the real solutions of each equation. 3x8=102CR3CRIn Problems 1-6, find the real solutions of each equation. 6 x 2 5x+1=05CR6CRIn Problems 7-9, solve each ineQuality. Graph the solution set. 23x68CR9CR10CR11CR12CR13CR14CR15CR16CR17CR18CR19CRThe inequality 1x3 can be written in interval notation as _______________. (pp. A76-A77)If x=2 , the value of the expression 3 x 2 5x+ 1 x is _____________. (pp. A6-A7)The domain of the variable in the expression x3 x+4 is ________________. (p.A7)Solve the inequality: 32x5 . Graph the solution set. (pp. A79-A80)If f is a function defined by the equation y=f( x ) , then x is called the _________ variable, and y is the _________ variable.6AYUIf the domain of f is all real numbers in the interval [ 0,7 ] , and the domain of g is all real numbers in the interval [ 2,5 ] , then the domain of f+g is all real numbers in the interval _______.The domain of f g consists of numbers x for which g( x ) ____________ 0 that are in the domains of both _________ and _____________.If f( x )=x+1 and g( x )= x 3 , then _______ = x 3 ( x+1 ) .True or False Every relation is a function.True or False The domain of ( fg )( x ) consists of the numbers x that are in the domains of both f and g .12AYUTrue or False If no domain is specified for a function f , then the domain of f is taken to be the set of real numbers.True or False The domain of the function f( x )= x 2 4 x is { x| x2 } .In Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function.In Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function.In Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function.In Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function.In Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function. ( 2,6 ),( 3,6 ),( 4,9 ),( 2,10 )In Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function. ( 2,5 ),( 1,3 ),( 3,7 ),( 4,12 )In Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function. ( 1,3 ),( 2,3 ),( 3,3 ),( 4,3 )In Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function. ( 0,2 ),( 1,3 ),( 2,3 ),( 3,7 )23AYU24AYU25AYU26AYUIn Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function. y=2 x 2 3x+4