91Ó°ÊÓ

Graph the function. $$ f(x)=\left\\{\begin{array}{ll} \sqrt{4+x}, & x<0 \\ \sqrt{4-x}, & x \geq 0 \end{array}\right. $$

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. $$ f(x)=-2 x^{2}+9 x $$

Graph the function. $$ f(x)=\left\\{\begin{array}{ll} 1-(x-1)^{2}, & x \leq 2 \\ \sqrt{x-2}, & x>2 \end{array}\right. $$

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope \(m\). Sketch the line. \((-10,4), \quad m\) is undefined.

Write an equation for the function that is described by the given characteristics. The shape of \(f(x)=|x|\), but shifted four units to the left and eight units downward

Find all real values of \(x\) such that \(f(x)=0\). $$ f(x)=5 x+1 $$

(a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=x^{3 / 5} $$

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$ y=x^{2}+x-2 $$

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$ y \equiv \frac{2 x}{x-1} $$

Write an equation for the function that is described by the given characteristics. The shape of \(f(x)=\sqrt{x}\), but shifted six units to the left and reflected in both the \(x\) -axis and the \(y\) -axis