In Exercises $1-4,$ match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).]

$$

y=-\frac{3}{2} x+3

$$

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In Exercises $1-4,$ match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).]

$$

y=\sqrt{9-x^{2}}

$$

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In Exercises $1-4,$ match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).]

$$

y=3-x^{2}

$$

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In Exercises $1-4,$ match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).]

$$

y=x^{3}-x

$$

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In Exercises $9-14,$ sketch the graph of the equation by point plotting.

$$

y=\frac{1}{2} x+2

$$

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In Exercises $9-14,$ sketch the graph of the equation by point plotting.

$$

y=5-2 x

$$

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In Exercises $9-14,$ sketch the graph of the equation by point plotting.

$$

y=4-x^{2}

$$

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In Exercises $9-14,$ sketch the graph of the equation by point plotting.

$$

y=(x-3)^{2}

$$

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In Exercises $9-14,$ sketch the graph of the equation by point plotting.

$$

y=|x|-1

$$

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In Exercises $9-14,$ sketch the graph of the equation by point plotting.

$$

y=|x|-1

$$

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In Exercises $9-14,$ sketch the graph of the equation by point plotting.

$$

y=\sqrt{x}-6

$$

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In Exercises $9-14,$ sketch the graph of the equation by point plotting.

$$

y=\sqrt{x+2}

$$

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In Exercises $9-14,$ sketch the graph of the equation by point plotting.

$$

y=\frac{3}{x}

$$

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In Exercises $9-14,$ sketch the graph of the equation by point plotting.

$$

y=\frac{1}{x+2}

$$

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In Exercises 15 and $16,$ describe the viewing window that yields the figure.

$$

y=x^{3}+4 x^{2}-3

$$

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In Exercises 15 and $16,$ describe the viewing window that yields the figure.

$$

y=|x|+|x-16|

$$

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In Exercises 17 and $18,$ use a graphing utility to graph the equation. Move the cursor along the curve to approximate the unknown coordinate of each solution point accurate to two decimal places.

$$

y=\sqrt{5-x} \quad(\text { a) }(2, y) \quad \text { (b) }(x, 3)

$$

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In Exercises 17 and $18,$ use a graphing utility to graph the equation. Move the cursor along the curve to approximate the unknown coordinate of each solution point accurate to two decimal places.

$$

y=x^{5}-5 x \quad \text { (a) }(-0.5, y) \quad \text { (b) }(x,-4)

$$

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In Exercises $19-28$ , find any intercepts.

$$

y=\frac{2-\sqrt{x}}{5 x}

$$

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In Exercises $19-28$ , find any intercepts.

$$

y=\frac{x^{2}+3 x}{(3 x+1)^{2}}

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

y=x^{2}-6

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

y=x^{2}-x

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

y^{2}=x^{3}-8 x

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

y=x^{3}+x

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

x y=4

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

x y^{2}=-10

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

y=4-\sqrt{x+3}

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

x y-\sqrt{4-x^{2}}=0

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

y=\frac{x}{x^{2}+1}

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

y=\frac{x^{2}}{x^{2}+1}

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

y=\left|x^{3}+x\right|

$$

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In Exercises $29-40,$ test for symmetry with respect to each axis and to the origin.

$$

|y|-x=3

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=2-3 x

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=-\frac{3}{2} x+6

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=\frac{1}{2} x-4

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=\frac{2}{3} x+1

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=9-x^{2}

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=x^{2}+3

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=(x+3)^{2}

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=2 x^{2}+x

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=x^{3}+2

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=x^{3}-4 x

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=x \sqrt{x+5}

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=\sqrt{25-x^{2}}

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

x=y^{3}

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

x=y^{2}-4

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=\frac{8}{x}

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=\frac{10}{x^{2}+1}

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=6-|x|

$$

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In Exercises $41-58,$ sketch the graph of the equation. Identify any intercepts and test for symetry.

$$

y=|6-x|

$$

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In Exercises $59-62$ , use a graphing utility to graph the equation. Identify any intercepts and test for symmetry.

$$

y^{2}-x=9

$$

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In Exercises $59-62$ , use a graphing utility to graph the equation. Identify any intercepts and test for symmetry.

$$

x^{2}+4 y^{2}=4

$$

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In Exercises $59-62$ , use a graphing utility to graph the equation. Identify any intercepts and test for symmetry.

$$

x+3 y^{2}=6

$$

Himanshu G.

Numerade Educator

In Exercises $59-62$ , use a graphing utility to graph the equation. Identify any intercepts and test for symmetry.

$$

3 x-4 y^{2}=8

$$

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In Exercises $63-70,$ find the points of intersection of the graphs of the equations.

$$

\begin{array}{c}{x+y=8} \\ {4 x-y=7}\end{array}

$$

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In Exercises $63-70,$ find the points of intersection of the graphs of the equations.

$$

\begin{array}{l}{3 x-2 y=-4} \\ {4 x+2 y=-10}\end{array}

$$

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In Exercises $63-70,$ find the points of intersection of the graphs of the equations.

$$

\begin{aligned} x^{2}+y &=6 \\ x+y &=4 \end{aligned}

$$

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$$

\begin{aligned} x^{2}+y &=6 \\ x+y &=4 \end{aligned}

$$

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In Exercises $63-70,$ find the points of intersection of the graphs of the equations.

$$

\begin{aligned} x^{2}+y^{2} &=5 \\ x-y &=1 \end{aligned}

$$

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In Exercises $63-70,$ find the points of intersection of the graphs of the equations.

$$

\begin{array}{c}{x^{2}+y^{2}=25} \\ {-3 x+y=15}\end{array}

$$

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In Exercises $63-70,$ find the points of intersection of the graphs of the equations.

$$

\begin{array}{l}{y=x^{3}} \\ {y=x}\end{array}

$$

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In Exercises $63-70,$ find the points of intersection of the graphs of the equations.

$$

\begin{array}{l}{y=x^{3}-4 x} \\ {y=-(x+2)}\end{array}

$$

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In Exercises $71-74,$ use a graphing utility to find the points of intersection of the graphs. Check your results analytically.

$$

\begin{array}{l}{y=x^{3}-2 x^{2}+x-1} \\ {y=-x^{2}+3 x-1}\end{array}

$$

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In Exercises $71-74,$ use a graphing utility to find the points of intersection of the graphs. Check your results analytically.

$$

\begin{array}{l}{y=x^{4}-2 x^{2}+1} \\ {y=1-x^{2}}\end{array}

$$

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In Exercises $71-74,$ use a graphing utility to find the points of intersection of the graphs. Check your results analytically.

$$

\begin{array}{l}{y=\sqrt{x+6}} \\ {y=\sqrt{-x^{2}-4 x}}\end{array}

$$

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In Exercises $71-74,$ use a graphing utility to find the points of intersection of the graphs. Check your results analytically.

$$

\begin{array}{l}{y=-|2 x-3|+6} \\ {y=6-x}\end{array}

$$

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Modeling Data The table shows the Consumer Price Index (CPI) for selected years. (Source: Bureau of Labor Statistics)

$$

\begin{array}{|c|c|c|c|c|c|c|}\hline \text { Year } & {1975} & {1980} & {1985} & {1990} & {1995} & {2000} & {2005} \\ \hline \mathrm{CPI} & {53.8} & {82.4} & {107.6} & {130.7} & {152.4} & {172.2} & {195.3} \\ \hline\end{array}

$$

(a) Use the regression capabilities of a graphing utility to find

a mathematical model of the form $y=a t^{2}+b t+c$ for the data. In the model, $y$ represents the CPI and $t$ represents the year, with $t=5$ corresponding to $1975 .$

(b) Use a graphing utility to plot the data and graph the model. Compare the data with the model.

(c) Use the model to predict the CPI for the year 2010.

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Modeling Data The table shows the numbers of cellular phone subscribers (in millions) in the United States for selected years. (Source: Cellular Telecommunications and Intemet Association)

$$

\begin{array}{|c|c|c|c|c|c|c|}\hline \text { Year } & {1990} & {1993} & {1996} & {1999} & {2002} & {2005} \\ \hline \text { Number } & {5} & {16} & {44} & {86} & {141} & {208} \\ \hline\end{array}

$$

(a) Use the regression capabilities of a graphing utility to find a mathematical model of the form $y=a t^{2}+b t+c$ for the data. In the model, $y$ represents the number of subscribers and $t$ represents the year, with $t=0$ corresponding to $1990 .$

(b) Use a graphing utility to plot the data and graph the model. Compare the data with the model.

(c) Use the model to predict the number of cellular phone subscribers in the United States in the year 2015 .

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Break-Even Point Find the sales necessary to break even $(R=C)$ if the cost $C$ of producing $x$ units is $C=5.5 \sqrt{x}+10,000$

and the revenue $R$ from selling $x$ units is

$R=3.29 x$

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Copper Wire The resistance $y$ in ohms of 1000 feet of solid copper wire at $77^{\circ} \mathrm{F}$ can be approximated by the model

$$y=\frac{10,770}{x^{2}}-0.37, \quad 5 \leq x \leq 100$$

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In Exercises 79 and $80,$ write an equation whose graph has the indicated property. (There may be more than one correct answer.)

The graph has intercepts at $x=-4, x=3,$ and $x=8$

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In Exercises 79 and $80,$ write an equation whose graph has the indicated property. (There may be more than one correct answer.)

The graph has intercepts at $x=-\frac{3}{2}, x=4,$ and $x=\frac{5}{2}$

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(a) Prove that if a graph is symmetric with respect to the $x$ -axis and to the $y$ -axis, then it is symmetric with respect to the origin. Give an example to show that the converse is not true.

(b) Prove that if a graph is symmetric with respect to one axis and to the origin, then it is symmetric with respect to the other axis.

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Match the equation or equations with the given characteristic.

$\begin{array}{ll}{\text { (i) } y=3 x^{3}-3 x} & {\text { (ii) } y=(x+3)^{2} \quad \text { (iii) } y=3 x-3} \\ {\text { (iv) } y=\sqrt[3]{x}} & {\text { (v) } y=3 x^{2}+3 \quad \text { (vi) } y=\sqrt{x+3}}\end{array}$

(a) Symmetric with respect to the $y$ -axis

(b) Three $x$ -intercepts

(c) Symmetric with respect to the $x$ -axis

(d) $(-2,1)$ is a point on the graph

(e) Symmetric with respect to the origin

(f) Graph passes through the origin

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True or False? In Exercises $83-86$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $(-4,-5)$ is a point on a graph that is symmetric with respect to the $x$ -axis, then $(4,-5)$ is also a point on the graph.

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True or False? In Exercises $83-86$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $(-4,-5)$ is a point on a graph that is symmetric with respect to the $y$ -axis, then $(4,-5)$ is also a point on the graph.

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True or False? In Exercises $83-86$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $b^{2}-4 a c>0$ and $a \neq 0$ , then the graph of $y=a x^{2}+b x+c$ has two $x$ -intercepts.

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If $b^{2}-4 a c=0$ and $a \neq 0,$ then the graph of $y=a x^{2}+b x+c$ has only one $x$ -intercept.

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In Exercises 87 and $88,$ find an equation of the graph that consists of all points $(x, y)$ having the given distance from the origin. (For a review of the Distance Formula, see Appendix C.)

The distance from the origin is twice the distance from $(0,3)$

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In Exercises 87 and $88,$ find an equation of the graph that consists of all points $(x, y)$ having the given distance from the origin. (For a review of the Distance Formula, see Appendix C.)

The distance from the origin is $K(K \neq 1)$ times the distance from $(2,0) .$

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