91Ó°ÊÓ

\(21-44\) . Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. $$ f(x)=x^{2}-1 $$

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

Assume that \(f\) is a one-to-one function. $$ \begin{array}{l}{\text { (a) If } f(2)=7, \text { find } f^{-1}(7)} \\ {\text { (b) If } f^{-1}(3)=-1, \text { find } f(-1)}\end{array} $$

A linear function is given.(a) Find the average rate of change of the function between \(x=a\) and \(x=a+h .\) (b) Show that the average rate of change is the same as the slope of the line. $$ f(x)=\frac{1}{2} x+3 $$

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

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

A linear function is given.(a) Find the average rate of change of the function between \(x=a\) and \(x=a+h .\) (b) Show that the average rate of change is the same as the slope of the line. $$ g(x)=-4 x+2 $$

Assume that \(f\) is a one-to-one function. $$ \begin{array}{l}{\text { (a) If } f(5)=18, \text { find } f^{-1}(18)} \\\ {\text { (b) If } f^{-1}(4)=2, \text { find } f(2)}\end{array} $$

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

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