91Ó°ÊÓ

(a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a). $$ f(x)=x \sqrt{x+3} $$

In Exercises 39-48, evaluate the expression. $$ -3|-3| $$

$$ f(x)= \begin{cases}1-(x-1)^{2}, & x \leq 2 \\ \sqrt{x-2}, & x>2\end{cases} $$

In Exercises 39-54, (a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=x^{2}-2, \quad x \leq 0 $$

Solve the equation and check your solution. (If not possible, explain why.) $$ (x+1)^{2}+2(x-2)=(x+1)(x-2) $$

\(f(x)=5 x+1\)

Write an equation for the function that is described by the given characteristics. The shape of \(f(x)=x^{3}\), but moved six units to the left, six units downward, and reflected in the \(y\)-axis.

In Exercises 39-54, (a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{4}{x} $$

\(f(x)=\frac{3 x-4}{5}\)

$$ f(x)= \begin{cases}x^{2}+5, & x \leq 1 \\ -x^{2}+4 x+3, & x>1\end{cases} $$