Chapter 3

Represent the data graphically. The average monthly temperatures (in \(^{\circ} \mathrm{C}\) ) for Washington, D.C., are as follows: $$\begin{array}{l|c|c|c|c|c|c|c|c|c|c|c|c} \text {Month} & \mathrm{J} & \mathrm{F} & \mathrm{M} & \mathrm{A} & \mathrm{M} & \mathrm{J} & \mathrm{J} & \mathrm{A} & \mathrm{S} & \mathrm{O} & \mathrm{N} & \mathrm{D} \\ \hline \text {Temp.}\left(^{\circ} \mathrm{C}\right) & 6 & 7 & 12 & 18 & 24 & 28 & 31 & 29 & 26 & 19 & 13 & 7 \end{array}$$

Make the given changes in the indicated examples of this section and then plot the graphs. In Example \(2,\) change \(2 x^{2}-4\) to \(4-2 x^{2}\)

Represent the data graphically. The exchange rate for the number of Canadian dollars equal to one U.S. dollar for \(1998-2012\) is as follows: $$\begin{array}{l|l|l|l|l|l|l|l|l} \text {Year} & 1998 & 2000 & 2002 & 2004 & 2006 & 2008 & 2010 & 2012 \\ \hline \text {Can. Dol.} & 1.48 & 1.49 & 1.57 & 1.30 & 1.13 & 1.07 & 1.04 & 1.02 \end{array}$$

Represent the data graphically. The amount of material necessary to make a cylindrical gallon container depends on the diameter, as shown in this table: $$\begin{array}{c|c|c|c|c|c|c|c} \text {Diameter (in.) } & 3.0 & 4.0 & 5.0 & 6.0 & 7.0 & 8.0 & 9.0 \\ \hline \text { Material in. }^{2} & 322 & 256 & 224 & 211 & 209 & 216 & 230 \end{array}$$

Represent the data graphically. An oil burner propels air that has been heated to \(90^{\circ} \mathrm{C}\). The temperature then drops as the distance from the burner increases, as shown in the following table: $$\begin{array}{l|r|r|r|r|r|r|r} \text {Distance (m)} & 0.0 & 1.0 & 2.0 & 3.0 & 4.0 & 5.0 & 6.0 \\ \hline \text {Temperature }\left(^{\circ} \mathrm{C}\right) & 90 & 84 & 76 & 66 & 54 & 46 & 41 \end{array}$$

Represent the data graphically. A changing electric current in a coil of wire will induce a voltage in a nearby coil. Important in the design of transformers, the effect is called mutual inductance. For two coils, the mutual inductance (in \(\mathrm{H}\) ) as a function of the distance between them is given in the following table: $$\begin{array}{l|r|r|r|r|r|r|r} \text {Distance }(\mathrm{cm}) & 0.0 & 2.0 & 4.0 & 6.0 & 8.0 & 10.0 & 12.0 \\ \hline M . \text {ind.}(\mathrm{H}) & 0.77 & 0.75 & 0.61 & 0.49 & 0.38 & 0.25 & 0.17 \end{array}$$

Graph the given functions. $$y=3 x$$

Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. $$y=3 x-1$$

Find the indicated functions. Express the area \(A\) of a circle as a function of (a) its radius \(r\) and (b) its diameter \(d\)

In Exercises \(5-36,\) graph the given functions. $$y=3 x$$

Plot the given points. $$\begin{aligned} &A(2,7), B(-1,-2),\\\ &C(-4,2), D(0,4) \end{aligned}$$

Find the domain and range of the given functions. In Exercises 11 and \(12,\) explain your answers. $$f(x)=x+5$$

Find the domain and range of the given functions. $$f(x)=x+5$$

Represent the data graphically. The temperatures felt by the body as a result of the wind-chill factor for an outside temperature of \(20^{\circ} \mathrm{F}\) (as determined by the National Weather Service) are given in the following table: $$\begin{array}{l|c|c|c|c|c|c|c|c} \text {Wind speed }(\mathrm{mi} / \mathrm{h}) & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 \\ \hline \text {Temp. felt }\left(^{\circ} \mathrm{F}\right) & 13 & 9 & 6 & 4 & 3 & 1 & 0 & -1 \end{array}$$

Graph the given functions. $$y=-2 x$$

Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. $$y=4-0.5 x$$

Find the indicated functions. Express the circumference \(c\) of a circle as a function of (a) its radius \(r\) and \((b)\) its diameter \(d\)

In Exercises \(5-36,\) graph the given functions. $$y=-2 x$$

Plot the given points. $$\begin{array}{l} A\left(3, \frac{1}{2}\right), B(-6,0), \\ C\left(-\frac{5}{2},-5\right), D(1,-3) \end{array}$$

Plot the given points. $$\begin{aligned} &A\left(3, \frac{1}{2}\right), B(-6,0)\\\ &C\left(-\frac{5}{2},-5\right), D(1,-3) \end{aligned}$$

Find the domain and range of the given functions. In Exercises 11 and \(12,\) explain your answers. $$g(u)=3-4 u^{2}$$

Find the domain and range of the given functions. $$g(u)=3-4 u^{2}$$

Represent the data graphically. The time required for a sum of money to double in value, when compounded annually, is given as a function of the interest rate in the following table: $$\begin{array}{l|c|c|c|c|c|c|c} \text {Rate (%)} & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text {Time (years) } & 17.7 & 14.2 & 11.9 & 10.2 & 9.0 & 8.0 & 7.3 \end{array}$$

Graph the given functions. $$y=2 x-4$$

Find the indicated functions. Express the diameter \(d\) of a sphere as a function of its volume \(V\)

Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. $$y=x^{2}-4 x$$

Plot the given points and then join these points, in the order given, by straight-line segments. Name the geometric figure formed. A(-1,4), B(3,4), C(2,-2), A(-1,4)

In Exercises \(5-36,\) graph the given functions. $$y=2 x-4$$

Find the domain and range of the given functions. $$G(R)=\frac{3.2}{R}$$

Find the domain and range of the given functions. In Exercises 11 and \(12,\) explain your answers. $$G(R)=\frac{3.2}{R}$$

Represent the data graphically. The torque \(T\) of an engine, as a function of the frequency \(f\) of rotation, was measured as follows: $$\begin{array}{c|c|c|c|c|c|c|c} f(\mathrm{r} / \mathrm{min}) & 500 & 1000 & 1500 & 2000 & 2500 & 3000 & 3500 \\\ \hline T(\mathrm{ft} \cdot 1 \mathrm{b}) & 175 & 90 & 62 & 45 & 34 & 31 & 27 \end{array}$$

Find the indicated functions. Express the edge \(e\) of a cube as a function of its surface area \(A\)

Graph the given functions. $$y=4-3 x$$

Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. $$y=8-2 x^{2}$$

Plot the given points and then join these points, in the order given, by straight-line segments. Name the geometric figure formed. $$A(0,3), B(0,-1), C(4,-1), A(0,3)$$

In Exercises \(5-36,\) graph the given functions. $$y=4-3 x$$

Find the domain and range of the given functions. $$F(r)=\sqrt{r+4}$$

Find the domain and range of the given functions. In Exercises 11 and \(12,\) explain your answers. $$F(r)=\sqrt{r+4}$$

Find the indicated functions. Express the area \(A\) of a square as a function of its diagonal \(d\); express the diagonal \(d\) of a square as a function of its area \(A\)

Graph the given functions. $$s=7-2 t$$

Plot the given points and then join these points, in the order given, by straight-line segments. Name the geometric figure formed. $$A(-2,-1), B(3,-1), C(3,5), D(-2,5), A(-2,-1)$$

In Exercises \(5-36,\) graph the given functions. $$s=7-2 t$$

Find the domain and range of the given functions. $$f(s)=\frac{2}{s^{2}}$$

Find the domain and range of the given functions. In Exercises 11 and \(12,\) explain your answers. $$f(s)=\frac{2}{s^{2}}$$

Graph the given functions. $$y=-3$$

Find the indicated functions. Express the perimeter \(p\) of a square as a function of its side \(s\) express the side \(s\) of a square as a function of its perimeter \(p\)

Display the graphs of the given functions on a graphing calculator. Use appropriate window settings. $$y=x^{4}-6 x^{2}$$

Plot the given points and then join these points, in the order given, by straight-line segments. Name the geometric figure formed. $$A(-5,-2), B(4,-2), C(6,3), D(-5,3), A(-5,-2)$$

In Exercises \(5-36,\) graph the given functions. $$y=-3$$

Find the domain and range of the given functions. $$T(t)=2 t^{4}+t^{2}-1$$