Chapter 3

\(5-12\) . A function \(f\) is given. (a) Use a graphing device to draw the graph of \(f\) . (b) State approximately the intervals on which \(f\) is increasing and on which \(f\) is decreasing. $$ f(x)=x^{4}-16 x^{2} $$

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

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=-x^{2}+6 x+4 $$

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

\(5-12\) . A function \(f\) is given. (a) Use a graphing device to draw the graph of \(f\) . (b) State approximately the intervals on which \(f\) is increasing and on which \(f\) is decreasing. $$ f(x)=x^{3}+2 x^{2}-x-2 $$

Complete the table. $$ f(x)=2(x-1)^{2} $$ $$ \begin{array}{|c|c|}\hline x & {f(x)} \\ \hline-1 & {} \\ {0} & {} \\ {1} & {} \\ {2} & {} \\ {3} & {} \\ \hline\end{array} $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=-x^{2}-4 x+4 $$

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

\(5-12\) . A function \(f\) is given. (a) Use a graphing device to draw the graph of \(f\) . (b) State approximately the intervals on which \(f\) is increasing and on which \(f\) is decreasing. $$ f(x)=x^{4}-4 x^{3}+2 x^{2}+4 x-3 $$

Complete the table. $$ g(x)=|2 x+3| $$ $$ \begin{array}{|c|c|}\hline x & {g(x)} \\ \hline-3 & {} \\ {-2} & {} \\ {0} & {} \\ {1} & {} \\ {3} & {} \\ \hline\end{array} $$

\(13-16\) Draw the graphs of \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$ f(x)=\sqrt{1+x}, \quad g(x)=\sqrt{1-x} $$

Sketch the graph of the function by first making a table of values. $$ F(x)=\frac{1}{x} $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=2 x^{2}+4 x+3 $$

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

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

\(13-16\) Draw the graphs of \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$ f(x)=x^{2}, \quad g(x)=\sqrt{x} $$

Sketch the graph of the function by first making a table of values. $$ F(x)=\frac{1}{x+4} $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=-3 x^{2}+6 x-2 $$

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

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

\(13-16\) Draw the graphs of \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$ f(x)=x^{2}, \quad g(x)=\frac{1}{3} x^{3} $$

Sketch the graph of the function by first making a table of values. $$ H(x)=|2 x| $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=2 x^{2}-20 x+57 $$

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

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

\(13-16\) Draw the graphs of \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$ f(x)=\sqrt[4]{1-x}, \quad g(x)=\sqrt{1-\frac{x^{2}}{9}} $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=2 x^{2}+x-6 $$

Sketch the graph of the function by first making a table of values. $$ H(x)=|x+1| $$

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

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

\(17-22=\) Use \(f(x)=3 x-5\) and \(g(x)=2-x^{2}\) to evaluate the expression. $$ \begin{array}{ll}{\text { (a) } f(g(0))} & {\text { (b) } g(f(0))}\end{array} $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=-4 x^{2}-16 x+3 $$

Sketch the graph of the function by first making a table of values. $$ G(x)=|x|+x $$

Assume \(f\) is a one-to-one function. (a) If \(f(2)=7,\) find \(f^{-1}(7)\) (b) If \(f^{-1}(3)=-1,\) find \(f(-1)\)

\(17-28\) A function is given. Determine the average rate of change of the function between the given values of the variable. $$ f(x)=3 x-2 ; \quad x=2, x=3 $$

Evaluate the function at the indicated values. $$ \begin{array}{l}{f(x)=2 x^{2}+3 x-4} \\ {f(0), f(2), f(-2), f(\sqrt{2}), f(x+1), f(-x)}\end{array} $$

\(17-22=\) Use \(f(x)=3 x-5\) and \(g(x)=2-x^{2}\) to evaluate the expression. $$ \begin{array}{ll}{\text { (a) } f(f(4))} & {\text { (b) } g(g(3))}\end{array} $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=6 x^{2}+12 x-5 $$

Sketch the graph of the function by first making a table of values. $$ G(x)=|x|-x $$

Assume \(f\) is a one-to-one function. (a) If \(f(5)=18,\) find \(f^{-1}(18)\) (b) If \(f^{-1}(4)=2,\) find \(f(2)\)

\(17-28\) A function is given. Determine the average rate of change of the function between the given values of the variable. $$ g(x)=5+\frac{1}{2} x ; \quad x=1, x=5 $$

Evaluate the function at the indicated values. $$ \begin{array}{l}{f(x)=x^{3}-4 x^{2}} \\ {f(0), f(1), f(-1), f\left(\frac{3}{2}\right), f\left(\frac{x}{2}\right), f\left(x^{2}\right)}\end{array} $$

\(17-22=\) Use \(f(x)=3 x-5\) and \(g(x)=2-x^{2}\) to evaluate the expression. $$ \begin{array}{ll}{\text { (a) }(f \circ g)(-2)} & {\text { (b) }(g \circ f)(-2)}\end{array} $$

19-28 \(=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$ f(x)=2 x-x^{2} $$

Sketch the graph of the function by first making a table of values. $$ f(x)=|2 x-2| $$

If \(f(x)=5-2 x,\) find \(f^{-1}(3)\)

\(17-28\) A function is given. Determine the average rate of change of the function between the given values of the variable. $$ h(t)=t^{2}+2 t ; \quad t=-1, t=4 $$

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

\(17-22=\) Use \(f(x)=3 x-5\) and \(g(x)=2-x^{2}\) to evaluate the expression. $$ \begin{array}{ll}{\text { (a) }(f \circ f)(-1)} & {\text { (b) }(g \circ g)(2)}\end{array} $$

19-28 \(=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$ f(x)=x+x^{2} $$