91Ó°ÊÓ

Determine a rational function that meets the given conditions, and sketch its graph. The function \(f\) has a vertical asymptote at \(x=2\), a horizontal asymptote at \(y=-2,\) and \(f(0)=0 .\)

Find the absolute extrema of each function, if they exist, over the indicated interval. Also indicate the \(x\) -value at which each extremum occurs. When no interval is specified, use the real numbers, \((-\infty, \infty)\). $$t(x)=x^{4}-2 x^{2}$$

Find the absolute extrema of each function, if they exist, over the indicated interval. Also indicate the \(x\) -value at which each extremum occurs. When no interval is specified, use the real numbers, \((-\infty, \infty)\). $$f(x)=2 x^{4}-4 x^{2}+2$$

Use a calculator's absolute-value feature to graph each function and determine relative extrema and intervals over which the function is increasing or decreasing. State any \(x\) -values at which the derivative does not exist. $$ f(x)=\left|x^{4}-2 x^{2}\right| $$

Find the absolute maximum and minimum values of each function, and sketch the graph. $$F(x)=\left\\{\begin{array}{ll}x^{2}+4, & \text { for }-2 \leq x<0 \\\4-x, & \text { for } 0 \leq x<3 \\\\\sqrt{x-2}, & \text { for } 3 \leq x \leq 67\end{array}\right.$$