Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
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+ 1 2In Problems 7998, find the slope and y-intercept of each line. Graph the line. x+2y=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, write an equation of each line. Express your answer using either the general form of the equation of a line, whichever you prefer.
In Problems 115118, write an equation of each line. Express your answer using either the general form of the equation of a line, whichever you prefer.In Problems 115118, write an equation of each line. Express your answer using either the general form of the equation of a line, whichever you prefer.In Problems, write an equation of each line. Express your answer using either the general 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?116AYUCost of Driving a Car The annual fixed costs of owning a small sedan are 4252, assuming the car is completely paid for. The cost to drive the car is approximately 0.14 per mile. Write a linear equation that relates the cost C and the number x of miles driven annually.118AYU Electricity Rates in Florida Florida Power & Light Company supplies electricity to residential customers for a monthly customer charge of plus cents per kilowatt hour (kWh) for up to kilowatt hours.
Write a linear equation that relates the monthly charge , in dollars, to the number of kilowatt hours used in a month,
Graph this equation.
What is the monthly charge for using kilowatt hours?
What is the monthly charge for using kilowatt hours?
Interpret the slope of the line.
120AYUMeasuring Temperature The relationship between Celsius (C) and Fahrenheit (F) degrees of measuring temperature is linear. Find a linear equation relating C and F if 0C corresponds to 32F and 100C corresponds to 212F. Use the equation to find the Celsius measure of 70F. Measuring Temperature The Kelvin scale for measuring temperature is obtained by adding to the Celsius temperature.
Write a linear equation relating and
Write a linear equation relating and (see Problem ).
Access Ramp A wooden access ramp is being built to reach a platform that sits inches above the floor. The ramp drops inches for every -inch run.
Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance from the platform.
Find and interpret the -intercept of the graph of your equation.
Design requirements stipulate that the maximum run be feet and that the maximum slope be a drop of inch for each inches of run. Will this ramp meet the requirements? Explain.
What slopes could be used to obtain the -inch rise and still meet design requirements?
U.S. Advertising Share A report showed that Internet ads accounted for 19 of all U.S. advertisement spending when print ads (magazines and newspapers) accounted for 26 of the spending. The report further showed that Internet ads accounted for 35 of all advertisement spending when print ads accounted for 16 of the spending. Write a linear equation that relates that percent y of print ad spending to the percent x of Internet ad spending. Find the intercepts of the graph of your equation. Do the intercepts have any meaningful interpretation? Predict the percent of print ad spending if Internet ads account for 39 of all advertisement spending in the United States.125AYU126AYU127AYU128AYU129AYUWhich 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+4131AYU132AYU133AYU134AYUCarpentry 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.136AYU137AYUWhat can you say about two lines that have equal slopes and equal y-intercept ?139AYU140AYU141AYU142AYU143AYU144AYUIn 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 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 =947AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYU64AYU65AYU1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE63RE64RE65RE66RE67RE68RE69RE70RE71RE72RE73RE74RE75RE1. Find the domain and range of each relation. Then determine whether each relation represents a function.
In Problems find the domain of each function and evaluate each function at
2.
In Problems 24, find the domain of each function and evaluate each function at x=1. g(x)=x+2x+2In Problems 24, find the domain of each function and evaluate each function at x=1. h(x)=x4x2+5x36Consider the graph of the function f below. Find the domain and the range of f. List the intercepts. Find f(1). For what value(s) of x does f(x)=3? Solve f(x)0.6. Graph the function on the interval using a graphing utility. Then approximate any local maximum and local minimum values rounded to two decimal places. Determine where the function is increasing and where it is decreasing.
Consider the function g(x)={2x+1ifx1x4ifx1 Graph the function. List the intercepts. Find g(5). Find g(2).For the function f(x)=3x23x+4, Find the average rate of change of f from 3to4. Find an equation of the secant line from 3to4.For the functions f(x)=2x2+1 and g(x)=3x2, find the following and simplify. (fg)(x) (f*g)(x) f(x+h)f(x)Graph each function using the techniques of shifting, compressing or stretching, and reflecting. Start with the graph of the basic function and show all the steps. h(x)=2(x+1)3+3 g(x)=x+4+2Find the difference quotient of f(x)=x23x.12. A community skating rink is in the shape of a rectangle with semicircles attached at the ends. The length of the rectangle is feet less than twice the width. The thickness of the ice is inches.
Build a model that expresses the ice volume as a function of the width,
How much ice is in the rink if the width is feet?
In Problems 1-6, find the real solutions of each equation. 3x8=10In Problems 1-6, find the real solutions of each equation. 3 x 2 x=0In Problems 1-6, find the real solutions of each equation. x 2 8x9=0In Problems 1-6, find the real solutions of each equation. 6 x 2 5x+1=0In Problems 1-6, find the real solutions of each equation. | 2x+3 |=4In Problems 1-6, find the real solutions of each equation. 2x+3 =2In Problems 7-9, solve each ineQuality. Graph the solution set. 23x6In Problems 7-9, solve each ineQuality. Graph the solution set. | 2x5 |3In Problems 7-9, solve each ineQuality. Graph the solution set. | 4x+1 |7(a) Find the distance from P 1 =( 2,3 )to P 2 =( 3,5 ) . (b) What is the midpoint of the line segment from P 1 to P 2 ? (c) What is the slope of the line containing the points P 1 and P 2 ?In problems 11-14, graph each equation. 3x2y=12In problems 11-14, graph each equation. x= y 2In problems 11-14, graph each equation. x 2 + ( y3 ) 2 =16In problems 11-14, graph each equation. y= x15CRFind the slope-intercept form of the equation of the line containing the points ( 2,4 )and( 6,8 ) .In problems 17-19, graph each function. f( x )= ( x+2 ) 2 3In problems 17-19, graph each function. f( x )= 1 xIn problems 17-19, graph each function. f( x )={ 2xifx2 | x |ifx2The 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)5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYUIn 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 )In Problems 2729, find the domain and range of each relation. Then determine whether the relation represents a function. (3,3),(3,5),(0,1),(4,6)In Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function. ( 4,4 ),( 3,3 ),( 2,2 ),( 1,1 )( 4,0 )In Problems 2729, find the domain and range of each relation. Then determine whether the relation represents a function. (1,8),(0,3),(2,1),(4,3)In Problems 19-30, state the domain and range for each relation. Then determine whether each relation represents a function. ( 2,16 ),( 1,4 ),( 0,3 ),( 1,4 )27AYUIn Problems 31-42, determine whether the equation defines y as a function of x. y= x 3In Problems 31-42, determine whether the equation defines y as a function of x. y= x 3In Problems 31-42, determine whether the equation defines y as a function of x . y=| x |In Problems , determine whether the equation defines as a function of
In Problems 31-42, determine whether the equation defines y as a function of x . y= 12xIn Problems 31-42, determine whether the equation defines y as a function of x . x= y 2In Problems 31-42, determine whether the equation defines y as a function of x . x+ y 2 =1In Problems 31-42, determine whether the equation defines y as a function of x . y= x 3In Problems 31-42, determine whether the equation defines y as a function of x . y= 3x1 x+2In Problems 3142, determine whether the equation defines y as a function of x. y=3x1x+2In Problems 31-42, determine whether the equation defines y as a function of x . x 2 4 y 2 =1In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )=3 x 2 +2x4In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )=2 x 2 +x1In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )= x x 2 +1In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )= x 2 1 x+4In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )=| x |+4In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )= x 2 + xIn problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )= 2x+1 3x5In problems 43-50, find the following for each function: (a) f( 0 ) (b) f( 1 ) (c) f( 1 ) (d) f( x ) (e) f( x ) (f) f( x+1 ) (g) f( 2x ) (h) f( x+h ) f( x )=1- 1 ( x+2 ) 2In Problems 51-66, find the domain of each function. f( x )=5x+4In Problems 51-66, find the domain of each function. f( x )= x 2 +2In Problems , find the domain of each function.
In Problems 51-66, find the domain of each function. f( x )= x 2 x 2 +1In Problems 51-66, find the domain of each function. g( x )= x x 2 -16In Problems 51-66, find the domain of each function. h( x )= 2x x 2 -4In Problems 51-66, find the domain of each function. F( x )= x-2 x 3 +xIn Problems 51-66, find the domain of each function. G( x )= x+4 x 3 -4xIn Problems 51-66, find the domain of each function. h( x )= 3x-12In Problems 51-66, find the domain of each function. G( x )= 1-xIn Problems 5170, find the domain of each function. p(x)=x2x+31In Problems , find the domain of each function.
In Problems 51-66, find the domain of each function. f( x )= x x-4In Problems 51-66, find the domain of each function. f( x )= x x-2