91Ó°ÊÓ

(a) Use a graphing utility to graph the function and visually determine the intervals on which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant on the intervals you identified in part (a). \(f(x)=x^{2 / 3}\)

Finding an Equation of a Line ,find an equation of the line that passes through the given point and has the indicated slope \(m .\) Sketch the line. $$(0,0), \quad m=4$$

\(\begin{array}{l}{\text { Finding and Analyzing Inverse Functions In }} \\\ {\text { Exercises } 45-56, \text { (a) find the inverse function of } f,} \\\ {\text { (b) graph both } f \text { and } f^{-1} \text { on the same set of coordinate }} \\ {\text { axes, (c) describe the relationship between the graphs of } f} \\ {\text { and } f^{-1}, \text { and (d) state the domains and ranges of } f \text { and } f^{-1}}\end{array}\) $$f(x)=3 x+1$$

Identifying a Parent Function In Exercises \(21-46\) , \(g\) is related to one of the parent functions described in Section 1.6 (a) Identify the parent function \(f\) . (b) Describe the sequence of transformations from \(f\) to \(g\) . (c) Sketch the graph of \(g\) (d) Use function notation to write \(g\) in terms of $$g(x)=\sqrt{3 x}+1$$

Identify any interepts and test for symmetry. Then sketch the graph of the equation. \(y=2 x-3\)

\(\begin{array}{l}{\text { Finding and Analyzing Inverse Functions In }} \\\ {\text { Exercises } 45-56, \text { (a) find the inverse function of } f,} \\\ {\text { (b) graph both } f \text { and } f^{-1} \text { on the same set of coordinate }} \\ {\text { axes, (c) describe the relationship between the graphs of } f} \\ {\text { and } f^{-1}, \text { and (d) state the domains and ranges of } f \text { and } f^{-1}}\end{array}\) $$f(x)=x^{5}-2$$

Writing an Equation from a Description In Exercises \(47-54\) , write an equation for the function described by the given characteristics. The shape of \(f(x)=x^{2},\) but shifted three units to the right and seven units down

Finding an Equation of a Line ,find an equation of the line that passes through the given point and has the indicated slope \(m .\) Sketch the line. $$(4,0), \quad m=-\frac{1}{3}$$

Finding Values for Which \(f(x)=g(x)\) In Exercises \(45-48,\) find the value(s) of \(x\) for which \(f(x)=g(x)\) . $$f(x)=x^{4}-2 x^{2}, \quad g(x)=2 x^{2}$$

Decomposing a composite Function, find two functions \(f\) and \(g\) such that \((f \circ g)(x)=h(x) .\) (There are many correct answers.) $$h(x)=(2 x+1)^{2}$$