91Ó°ÊÓ

For the following exercises, graph the absolute value function. Plot at least five points by hand for each graph. \(y=|x|+1\)

For the following exercises, determine whether the relation represents \(y\) as a function of \(x\). \(x^{2}+y^{2}=9\)

For the following exercises, use function composition to verify that \(f(x)\) and \(g(x)\) are inverse functions. \(f(x)=-3 x+5\) and \(g(x)=\frac{x-5}{-3}\)

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

For the following exercises, find the domain of each function using interval notation. \(f(x)=\frac{2 x^{3}-250}{x^{2}-2 x-15}\)

For the following exercises, use each set of functions to find \(f(g(h(x)))\). Simplify your answers. \(f(x)=x^{2}+1, g(x)=\frac{1}{x},\) and \(h(x)=x+3\)

For the following exercises, describe how the graph of the function is a transformation of the graph of the original function \(f\). \(y=f(x+4)-1\)

For the following exercises, determine whether the relation represents \(y\) as a function of \(x\). \(2 x y=1\)

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

For the following exercises, use each set of functions to find \(f(g(h(x)))\). Simplify your answers. Given \(f(x)=\frac{1}{x}\) and \(g(x)=x-3,\) find 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) \(\left(\frac{f}{g}\right)(x)\)