91Ó°ÊÓ

For the following exercises, determine whether the relation represents \(y\) as a function of \(x\). \(y=-2 x^{2}+40 x\)

For the following exercises, find the \(x\) - and \(y\) -intercepts of the graphs of each function. \(f(x)=|-2 x+1|-13\)

For the following exercises, describe how the graph of the function is a transformation of the graph of the original function \(f\). \(y=f(x)+5\)

For the following exercises, find a domain on which each function \(f\) is one- to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of \(f\) restricted to that domain. \(f(x)=(x-6)^{2}\)

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. \(r(t)=4 t^{3}\) on \([2,2+h]\)

For the following exercises, find the domain of each function using interval notation. \(f(x)=\frac{9}{x-6}\)

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

For the following exercises, use each pair of functions to find \(f(g(x))\) and \(g(f(x))\). Simplify your answers. \(f(x)=|x|, \quad g(x)=5 x+1\)

For the following exercises, find the domain of each function using interval notation. \(f(x)=\frac{3 x+1}{4 x+2}\)

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. \(\frac{f(x+h)-f(x)}{h}\) given \(f(x)=2 x^{2}-3 x\) on \([x, x+h]\)