Chapter 1

Graph each set of numbers on a number line. $$\\{-6,-5,-4,-3,-2\\}$$

Sketch the graph of \(f\) by hand. $$f(x)=\frac{1}{2} x$$

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. Through \((0,5)\) and \((10,0)\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Alcohol Mixture How many gallons of pure alcohol should be mixed with 20 gallons of a \(15 \%\) alcohol solution to obtain a mixture that is \(25 \%\) alcohol?

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$2 x-5=x+7$$

Graph each set of numbers on a number line. $$\left\\{-0.5,0.75, \frac{5}{3}, 3.5\right\\}$$

Sketch the graph of \(f\) by hand. $$f(x)=-\frac{2}{3} x$$

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. Through \((0,-8)\) and \((4,0)\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ A chemist wishes to strengthen a mixture from \(10 \%\) alcohol to \(30 \%\) alcohol. How much pure elcohol should be added to 7 liters of the \(10 \%\) mixture?

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$9 x-17=2 x+4$$

Graph each set of numbers on a number line. $$\left\\{-0.6, \frac{9}{8}, 2.5, \frac{13}{4}\right\\}$$

Sketch the graph of \(f\) by hand. $$f(x)=x^{2}$$

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. $$\begin{array}{c|c}x & y \\\\\hline-7 & -44 \\\\-6 & -36 \\\\-5 & -28 \\\\-4 & -20\end{array}$$

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Saline Solution Mixture How much water should be added to 8 milliliters of \(6 \%\) saline solution to reduce the concentration to \(4 \%\) saline?

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$0.01 x+3.1=2.03 x-2.96$$

Sketch the graph of \(f\) by hand. $$f(x)=|x|$$

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. $$\begin{array}{c|c}x & y \\\\\hline-2.4 & 5.2 \\\1.3 & -24.4 \\\1.75 & -28 \\\2.98 & -37.84\end{array}$$

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Acid Mixture How much water should be added to 20 liters of an \(18 \%\) acid solution to reduce the concentration to \(15 \%\) acid?

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$0.04 x+2.1=0.02 x+1.92$$

Using her calculator, a student found the decimal 1.414213562 when she evaluated \(\sqrt{2} .\) Is this decimal the exact value of \(\sqrt{2}\) or just an approximation of \(\sqrt{2} ?\) Should she write \(\sqrt{2}=1.414213562\) or \(\sqrt{2} \approx 1.414213562 ?\)

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(5,1),(3,2),(4,9),(7,6)\\}$$

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. $$\begin{array}{c|c}x & y \\\\\hline 2 & -5 \\\3 & -8 \\\4 & -11 \\\5 & -14\end{array}$$

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Antifreeze Mixture An automobile radiator holds 16 liters of fluid. There is currently a mixture in the radiator that is \(80 \%\) antifreeze and \(20 \%\) water. How much of this mixture should be drained and replaced by pure antifreeze so that the resulting mixture is \(90 \%\) antifreeze?

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$-(x+5)-(2+5 x)+8 x=3 x-5$$

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(2,3)$$

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(8,0),(5,4),(9,3),(3,8)\\}$$

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. $$\begin{array}{c|c}x & y \\\\\hline-1.1 & 1.5 \\\\-1.0 & 2.0 \\\\-0.9 & 2.5 \\\\-0.8 & 3.0\end{array}$$

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Antifreeze Mixture \(\quad\) An automobile radiator contains a 10 -quart mixture of water and antifreeze that is \(40 \%\) antifreeze. How much should the owner drain from the radiator and replace with pure antifreeze so that the liquid in the radiator will be \(80 \%\) antifreeze?

Also, give the (a) \(x\) -intercept (if any), (b) \(y\) -intercept (if anyy, (c) domain, (d) range, and (e) slope of the line (if defined). Do not use a calculator. \(x=2\)

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$-(8+3 x)+5=2 x+3$$

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(-1,2)$$

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(1,6),(2,6),(3,6)\\}$$

Graph each line by hand. Give the \(x\)- and y-intercepts. \(x-y=4\)

Exercises 27 and 28 involve octane rating of gasoline, a measure of its antiknock qualities. In one measure of octane, a standard fuel is made with only two ingredients: heptane and isooctane. For this type of fuel, the octane rating is the percent of isooctane. An actual gasoline blend is then compared with a standard fuel. For example, a gasoline with an octane rating of 98 has the same antiknock properties as a standard fuel that is \(98 \%\) isooctane. Octane Rating of Gasoline How many gallons of 94-octane gasoline should be mixed with 400 gallons of 99-octane gasoline to obtain a mixture that is 97-octane?

Also, give the (a) \(x\) -intercept (if any), (b) \(y\) -intercept (if anyy, (c) domain, (d) range, and (e) slope of the line (if defined). Do not use a calculator. \(x=2\)

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$\frac{2 x+1}{3}+\frac{x-1}{4}=\frac{13}{2}$$

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(-3,-2)$$

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(-10,5),(-20,5),(-30,5)\\}$$

Graph each line by hand. Give the \(x\)- and y-intercepts. \(x+y=4\)

Exercises 27 and 28 involve octane rating of gasoline, a measure of its antiknock qualities. In one measure of octane, a standard fuel is made with only two ingredients: heptane and isooctane. For this type of fuel, the octane rating is the percent of isooctane. An actual gasoline blend is then compared with a standard fuel. For example, a gasoline with an octane rating of 98 has the same antiknock properties as a standard fuel that is \(98 \%\) isooctane. How many gallons of 92-octane and 98 -octane gasoline should be mixed together to provide 120 gallons of 96 -octane gasoline?

Also, give the (a) \(x\) -intercept (if any), (b) \(y\) -intercept (if anyy, (c) domain, (d) range, and (e) slope of the line (if defined). Do not use a calculator. 2\(x=-3\)

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$\frac{x-2}{4}+\frac{x+1}{2}=1$$

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(1,-4)$$

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(4,1),(3,-5),(-2,3),(3,7)\\}$$

Graph each line by hand. Give the \(x\)- and y-intercepts. \(3 x-y=6\)

Solve each problem. Women against the Men For the men's Olympic 100-meter freestyle swimming event, winning times in seconds during year \(x\) can be approximated by the formula \(F(x)=-\frac{5}{44} x+276.18,\) where \(1948 \leq x \leq 2008\) (Assume that \(x\) is a multiple of 4 because the Olympics occur every 4 years.) (a) Evaluate \(F(2008)\) and interpret the result. (b) In 2008 the women's Olympic winning time for the 100 -meter freestyle was about 53 seconds. Determine the years when this time would have beaten or tied the men's winning times. (IMAGE CAN'T COPY)

$$\text { Solve each equation analytically. Check it analytically, and then support your solution graphically.}$$ $$\frac{1}{2}(x-3)=\frac{5}{12}+\frac{2}{3}(2 x-5)$$

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(0,5)$$

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(0,5),(1,3),(0,-4)\\}$$

Graph each line by hand. Give the \(x\)- and y-intercepts. \(2 x-3 y=6\)