91Ó°ÊÓ

For the following exercises, graph the given functions by hand. $$ y=-|x| $$

Determine the interval(s) on which the function is increasing and decreasing. $$f(x)=4(x+1)^{2}-5$$

Given \(f(x)=\frac{1}{x},\) and \(g(x)=x-3,\) find the following: a. \(\left(f_{0} g\right)(x)\) b. the domain of \((f \circ g)(x)\) in interval notation c. \((g \circ f)(x)\) d. the domain of \(\left(g_{\circ} f\right)(x)\) e. \(\left(\frac{f}{g}\right) x\)

Given \(f(x)=\frac{1}{x},\) and \(g(x)=x-3,\) fi \(\mathrm{d}\) the following: a. \((f \circ g)(x)\) b. the domain of \((f \circ g)(x)\) in interval notation c. \((g \circ f)(x)\) d. the domain of \((g \circ f)(x)\) e. \(\left(\frac{f}{g}\right) x\)

For the following exercises, use a graphing utility to determine whether each function is one-to-one. $$ f(x)=\sqrt[3]{3 x+1} $$

For the following exercises, find the domain of each function using interval notation. $$ f(x)=\frac{5}{\sqrt{x-3}} $$

For the following exercises, determine the interval \((s)\) on which the function is increasing and decreasing. $$ f(x)=4(x+1)^{2}-5 $$

Given \(f(x)=\sqrt{2-4 x}\) and \(g(x)=-\frac{3}{x},\) find the following: a. \((g \circ f)(x)\) b. the domain of \((g \circ f)(x)\) in interval notation

For the following exercises, graph the given functions by hand. $$ y=-|x|-2 $$

Determine the interval(s) on which the function is increasing and decreasing. $$g(x)=5(x+3)^{2}-2$$