Chapter 1

A car rental agency charges \(\$ 200\) per week plus \(\$ 0.15\) per mile to rent a car. a. Express the weekly cost to rent the car, \(f\), as a function of the number of miles driven during the week, \(x\). b. How many miles did you drive during the week if the weekly cost to rent the car was \(\$ 320 ?\)

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(2,3) \text { and }(14,8)$$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=4 x \text { and } g(x)=\frac{x}{4}$$

Find the domain of each function. $$f(x)=3(x-4)$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(4,7) \text { and }(8,10)$$

Plot the given point in a rectangular coordinate system. (1,4)

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(1,2),(3,4),(5,5)\\}$$

A car rental agency charges \(\$ 180\) per week plus \(\$ 0.25\) per mile to rent a car. a. Express the weekly cost to rent the car, \(f\), as a function of the number of miles driven during the week, \(x\). b. How many miles did you drive during the week if the weekly cost to rent the car was \(\$ 395 ?\)

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. (5,1) and (8,5)

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=6 x \text { and } g(x)=\frac{x}{6}$$

Find the domain of each function. $$f(x)=2(x+5)$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(2,1) \text { and }(3,4)$$

Plot the given point in a rectangular coordinate system. (2,5)

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(4,5),(6,7),(8,8)\\}$$

One yardstick for measuring how steadily-if slowlyathletic performance has improved is the mile run. In 1954 , Roger Bannister of Britain cracked the 4-minute mark, setting the record for running a mile in 3 minutes, 59.4 seconds, or 239.4 seconds in the half-century since then, the record has decreased by 0.3 second per year. a. Express the record time for the mile run, \(M,\) as a function of the number of years after \(1954, x\). b. If this trend continues, in which year will someone run a 3-minute, or 180 -second, mile?

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(4,-1) \text { and }(-6,3)$$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=3 x+8 \text { and } g(x)=\frac{x-8}{3}$$

Find the domain of each function. $$g(x)=\frac{3}{x-4}$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(-2,1) \text { and }(2,2)$$

Plot the given point in a rectangular coordinate system. $$(-2,3)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(3,4),(3,5),(4,4),(4,5)\\}$$

According to the National Center for Health Statistics, in \(1990,28 \%\) of babies in the United States were born to parents who were not married. Throughout the 1990 s, this percentage increased by approximately 0.6 per year. a. Express the percentage of babies born out of wedlock, \(P\), as a function of the number of years after \(1990, x\) b. If this trend continued, in which year were \(40 \%\) of babies born out of wedlock?

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(2,-3) \text { and }(-1,5)$$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=4 x+9 \text { and } g(x)=\frac{x-9}{4}$$

Find the domain of each function. $$g(x)=\frac{2}{x+5}$$

Plot the given point in a rectangular coordinate system. $$(-1,4)$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(-1,3) \text { and }(2,4)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(5,6),(5,7),(6,6),(6,7)\\}$$

The bus fare in a city is \(\$ 1.25 .\) People who use the bus have the option of purchasing a monthly discount pass for \(\$ 21.00 .\) With the discount pass, the fare is reduced to \(\$ 0.50\). a. Express the total monthly cost to use the bus without a discount pass, \(f,\) as a function of the number of times in a month the bus is used, \(x\). b. Express the total monthly cost to use the bus with a discount pass, \(g,\) as a function of the number of times in a month the bus is used, \(x\) c. Determine the number of times in a month the bus must be used so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass. What will be the monthly cost for each option?

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(0,0) \text { and }(-3,4)$$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=5 x-9 \text { and } g(x)=\frac{x+5}{9}$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-8,-10) and parallel to the line whose equation is \(y=-4 x+3\)

Find the domain of each function. $$f(x)=x^{2}-2 x-15$$

Plot the given point in a rectangular coordinate system. $$(-3,-5)$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(4,-2) \text { and }(3,-2)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(3,-2),(5,-2),(7,1),(4,9)\\}$$

A discount pass for a bridge costs \(\$ 21\) per month. The toll for the bridge is normally \(\$ 2.50\), but it is reduced to \(\$ 1\) for people who have purchased the discount pass. a. Express the total monthly cost to use the bridge without a discount pass, \(f,\) as a function of the number of times in a month the bridge is crossed, \(x\). b. Express the total monthly cost to use the bridge with a discount pass, \(g,\) as a function of the number of times in a month the bridge is crossed, \(x\). c. Determine the number of times in a month the bridge must be crossed so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass. What will be the monthly cost for each option?

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(0,0) \text { and }(3,-4)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-2,-7) and parallel to the line whose equation is \(y=-5 x+4\)

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=3 x-7 \text { and } g(x)=\frac{x+3}{7}$$

Find the domain of each function. $$f(x)=x^{2}+x-12$$

Plot the given point in a rectangular coordinate system. $$(-4,-2)$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(4,-1) \text { and }(3,-1)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(10,4),(-2,4),(-1,1),(5,6)\\}$$

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership of \(\$ 100\) and you pay \(80 \%\) of the manufacturer's recommended list price. Plan \(\mathbf{B}\) offers an annual membership fee of \(\$ 40\) and you pay \(90 \%\) of the manufacturer's recommended list price. a. Express the total yearly amount paid to the warehouse under plan \(\mathrm{A}, f,\) as a function of the dollars of merchandise purchased during the year, \(x\). b. Express the total yearly amount paid to the warehouse under plan \(\mathrm{B}, \mathrm{g}\), as a function of the dollars of merchandise purchased during the year, \(x\). c. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the total yearly amount paid to the warehouse for each plan?

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(-2,-6) \text { and }(3,-4)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (2,-3) and perpendicular to the line whose equation is \(y=\frac{1}{5} x+6\)

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=\frac{3}{x-4} \text { and } g(x)=\frac{3}{x}+4$$

Find the domain of each function. $$g(x)=\frac{3}{x^{2}-2 x-15}$$

Plot the given point in a rectangular coordinate system. $$(4,-1)$$