91Ó°ÊÓ

In Exercises 39-48, evaluate the expression. $$ \frac{x}{x+2}, \quad x<-2 $$

Write an equation for the function that is described by the given characteristics. The shape of \(f(x)=|x|\), but moved 10 units upward and reflected in the \(x\)-axis.

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line. \(\left(4, \frac{5}{2}\right)\) $$ \begin{aligned} & \text { Slope } \\ m &=3 \\ m &=-1 \\ m &=-2 \\ m &=4 \\ m &=-\frac{1}{3} \\ m &=\frac{3}{4} \end{aligned} $$ \(m\) is undefined. \(m\) is undefined. $$ \begin{aligned} &m=0 \\ &m=0 \\ &m=5 \\ &m=-\frac{5}{2} \end{aligned} $$

Complete the table. Use the resulting solution points to sketch the graph of the equation. \(y=-2 x+5\)

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 \(f^{-1}\). $$ f(x)=\frac{4}{x} $$

Find two functions \(f\) and \(g\) such that \((f \circ g)(x)=h(x)\). (There are many correct answers.) $$h(x)=(2 x+1)^{2}$$

(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). $$ f(x)=x^{3 / 2} $$

In Exercises 39-48, evaluate the expression. $$ \frac{|x-1|}{x-1}, \quad x>1 $$

$$ h(x)= \begin{cases}3-x^{2}, & x<0 \\ x^{2}+2, & x \geq 0\end{cases} $$

Complete the table. Use the resulting solution points to sketch the graph of the equation. \(y=x^2-3 x\)