Chapter 3

Sketch the graph of the function by first making a table of values. \(f(x)=x^{2}-4\)

\(9-18\) m function \(f\) is given. (a) Use a graphing calculator to draw the graph of \(f .(b)\) Find the domain and range of \(f\) from the graph. $$ f(x)=x^{2}, \quad-2 \leq x \leq 5 $$

Find the domain of the function. $$ b(x)=(x-3)^{-1 / 4} $$

Determine whether the function is one-to-one. $$ g(x)=\sqrt{x} $$

A function is given. Determine the average rate of change of the function between the given values of the variable. $$ f(x)=x^{3}-4 x^{2} ; \quad x=0, x=10 $$

\(5-14\) . Suppose the graph of \(f\) is given. Describe how the graph of each function can be obtained from the graph of \(f .\) \(\begin{array}{ll}{\text { (a) } y=f(4 x)} & {\text { (b) } y=f\left(\frac{1}{4} x\right)}\end{array}\)

Sketch the graph of the function by first making a table of values. \(h(x)=16-x^{2}\)

\(9-18\) m function \(f\) is given. (a) Use a graphing calculator to draw the graph of \(f .(b)\) Find the domain and range of \(f\) from the graph. $$ f(x)=4-x^{2} $$

Draw a machine diagram for the function. $$f(x)=\sqrt{x-1}$$

Find the domain of the function. $$ k(x)=\frac{\sqrt{x+3}}{x-1} $$

Determine whether the function is one-to-one. $$ g(x)=|x| $$

A function is given. Determine the average rate of change of the function between the given values of the variable. $$ f(x)=x+x^{4} ; \quad x=-1, x=3 $$

\(5-14\) . Suppose the graph of \(f\) is given. Describe how the graph of each function can be obtained from the graph of \(f .\) (a) \(y=f(2 x)-1 \quad\) (b) \(y=2 f\left(\frac{1}{2} x\right)\)

Sketch the graph of the function by first making a table of values. \(g(x)=(x-3)^{2}\)

\(9-18\) m function \(f\) is given. (a) Use a graphing calculator to draw the graph of \(f .(b)\) Find the domain and range of \(f\) from the graph. $$ f(x)=x^{2}+4 $$

Draw a machine diagram for the function. $$ f(x)=\frac{3}{x-2} $$

Determine whether the function is one-to-one. $$ h(x)=x^{2}-2 x $$

A function is given. Determine the average rate of change of the function between the given values of the variable. $$ f(x)=3 x^{2} ; \quad x=2, x=2+h $$

\(15-18\) Explain how the graph of \(g\) is obtained from the graph of \(f .\) $$ \begin{array}{l}{\text { (a) } f(x)=x^{2}, \quad g(x)=(x+2)^{2}} \\ {\text { (b) } f(x)=x^{2}, \quad g(x)=x^{2}+2}\end{array} $$

Sketch the graph of the function by first making a table of values. \(g(x)=x^{3}-8\)

\(9-18\) m function \(f\) is given. (a) Use a graphing calculator to draw the graph of \(f .(b)\) Find the domain and range of \(f\) from the graph. $$ f(x)=\sqrt{16-x^{2}} $$

Determine whether the function is one-to-one. $$ h(x)=x^{3}+8 $$

A function is given. Determine the average rate of change of the function between the given values of the variable. $$ f(x)=4-x^{2} ; \quad x=1, x=1+h $$

\(15-18\) Explain how the graph of \(g\) is obtained from the graph of \(f .\) $$ \begin{array}{l}{\text { (a) } f(x)=x^{3}, \quad g(x)=(x-4)^{3}} \\ {\text { (b) } f(x)=x^{3}, \quad g(x)=x^{3}-4}\end{array} $$

Sketch the graph of the function by first making a table of values. \(g(x)=(x+2)^{3}\)

\(9-18\) m function \(f\) is given. (a) Use a graphing calculator to draw the graph of \(f .(b)\) Find the domain and range of \(f\) from the graph. $$ f(x)=-\sqrt{25-x^{2}} $$

Draw the graphs of \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$ f(x)=\sqrt{1+x}, \quad g(x)=\sqrt{1-x} $$

Determine whether the function is one-to-one. $$ f(x)=x^{4}+5 $$

\(15-18\) Explain how the graph of \(g\) is obtained from the graph of \(f .\) $$ \begin{array}{l}{\text { (a) } f(x)=|x|, \quad g(x)=|x+2|-2} \\ {\text { (b) } f(x)=|x|, \quad g(x)=|x-2|+2}\end{array} $$

Sketch the graph of the function by first making a table of values. \(g(x)=x^{2}-2 x\)

\(9-18\) m function \(f\) is given. (a) Use a graphing calculator to draw the graph of \(f .(b)\) Find the domain and range of \(f\) from the graph. $$ f(x)=\sqrt{x-1} $$

Evaluate the function at the indicated values. $$ f(x)=x^{2}-6 ; \quad f(-3), f(3), f(0), f\left(\frac{1}{2}\right), f(10) $$

Draw the graphs of \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$ f(x)=x^{2}, \quad g(x)=\sqrt{x} $$

Determine whether the function is one-to-one. $$ f(x)=x^{4}+5, \quad 0 \leq x \leq 2 $$

A function is given. Determine the average rate of change of the function between the given values of the variable. $$ g(x)=\frac{2}{x+1} ; \quad x=0, x=h $$

\(15-18\) Explain how the graph of \(g\) is obtained from the graph of \(f .\) $$ \begin{array}{ll}{\text { (a) } f(x)=\sqrt{x},} & {g(x)=-\sqrt{x}+1} \\\ {\text { (b) } f(x)=\sqrt{x},} & {g(x)=\sqrt{-x}+1}\end{array} $$

Sketch the graph of the function by first making a table of values. \(h(x)=4 x^{2}-x^{4}\)

\(9-18\) m function \(f\) is given. (a) Use a graphing calculator to draw the graph of \(f .(b)\) Find the domain and range of \(f\) from the graph. $$ f(x)=\sqrt{x+2} $$

Evaluate the function at the indicated values. $$f(x)=x^{3}+2 x, \quad f(-2), f(1), f(0), f\left(\frac{1}{3}\right), f(0.2)$$

Draw the graphs of \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$ f(x)=x^{2}, \quad g(x)=\frac{1}{3} x^{3} $$

Determine whether the function is one-to-one. $$ f(x)=\frac{1}{x^{2}} $$

A function is given. Determine the average rate of change of the function between the given values of the variable. $$ f(t)=\frac{2}{t} ; \quad t=a, t=a+h $$

Sketch the graph of the function by first making a table of values. \(f(x)=1+\sqrt{x}\)

Evaluate the function at the indicated values. $$ \begin{array}{l}{f(x)=2 x+1} \\ {f(1), f(-2), f\left(\frac{1}{2}\right), f(a), f(-a), f(a+b)}\end{array} $$

Draw the graphs of \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$ f(x)=\sqrt[4]{1-x}, g(x)=\sqrt{1-\frac{x^{2}}{9}} $$

Determine whether the function is one-to-one. $$ f(x)=\frac{1}{x} $$

A function is given. Determine the average rate of change of the function between the given values of the variable. $$ f(t)=\sqrt{t}, \quad t=a, t=a+h $$

Sketch the graph of the function by first making a table of values. \(f(x)=\sqrt{x+4}\)

Evaluate the function at the indicated values. $$ \begin{array}{l}{f(x)=x^{2}+2 x} \\ {f(0), f(3), f(-3), f(a), f(-x), f\left(\frac{1}{a}\right)}\end{array} $$

Use \(f(x)=3 x-5\) and \(g(x)=2-x^{2}\) to evaluate the expression. $$ \begin{array}{ll}{\text { (a) } f(g(0))} & {\text { (b) } g(f(0))}\end{array} $$