91Ó°ÊÓ

For the following exercises, determine the domain for each function in interval notation. Given \(f(x)=\sqrt{x}\) and \(g(x)=|x-3|,\) find \(\frac{g}{f}\)

For the following exercises, find the average rate of change of each function on the interval specified for real numbers \(b\) or \(h\) in simplest form. $$ g(x)=3 x^{2}-2 \text { on }[x, x+h] $$

For the following exercises, determine whether the relation represents \(y\) as a function of \(x\). $$ 3 x^{2}+y=14 $$

For the following exercises, find the \(x\) - and \(y\) -intercepts of the graphs of each function. $$ f(x)=-2|x+1|+6 $$

For the following exercises, find the domain of each function using interval notation. $$ f(x)=\sqrt{x^{2}+4} $$

For the following exercises, describe how the graph of the function is a transformation of the graph of the original function \(f\). $$ y=f(x+43) $$

For the following exercise, fi d the indicated function given \(f(x)=2 x^{2}+1\) and \(g(x)=3 x-5\). a. \(f(g(2))\) b. \(f(g(x))\) c. \(g(f(x))\) d. \((g \circ g)(x)\) e. \((f \circ f)(-2)\)

For the following exercises, find the average rate of change of each function on the interval specified for real numbers \(b\) or \(h\) in simplest form. $$ a(t)=\frac{1}{t+4} \text { on }[9,9+h] $$

For the following exercises, find \(f^{-1}(x)\) for each function. $$ f(x)=\frac{x}{x+2} $$

Describe how the graph of the function is a transformation of the graph of the original function \(f.\) $$y=f(x+43)$$