91Ó°ÊÓ

Sketch a graph of the piecewise defined function. $$f(x)=\left\\{\begin{array}{ll} 0 & \text { if }|x| \leq 2 \\ 3 & \text { if }|x|>2 \end{array}\right.$$

Difference Quotient Find \(f(a), f(a+h),\) and the difference quotient \(\frac{f(a+h)-f(a)}{h},\) where \(h \neq 0.\) $$f(x)=5-2 x$$

Difference Quotient Find \(f(a), f(a+h),\) and the difference quotient \(\frac{f(a+h)-f(a)}{h},\) where \(h \neq 0.\) $$f(x)=3 x^{2}+2$$

Graphing Transformations Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. $$y=\frac{1}{2}|x|$$

Use the Inverse Function Property to show that \(f\) and \(g\) are inverses of each other. $$f(x)=x^{3}+1 ; g(x)=(x-1)^{1 / 3}$$

Use the table to evaluate the expression. $$\begin{array}{|c|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5 & 6 \\\\\hline f(x) & 2 & 3 & 5 & 1 & 6 & 3 \\\\\hline g(x) & 3 & 5 & 6 & 2 & 1 & 4 \\\\\hline\end{array}$$ $$(g \circ f)(2)$$

Sketch a graph of the piecewise defined function. $$f(x)=\left\\{\begin{array}{ll} x^{2} & \text { if }|x| \leq 1 \\ 1 & \text { if }|x|>1 \end{array}\right.$$

Graphing Transformations Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. $$y=(x-3)^{2}+5$$

Use the Inverse Function Property to show that \(f\) and \(g\) are inverses of each other. $$f(x)=\frac{1}{x-1} ; \quad g(x)=\frac{1}{x}+1$$

Use the table to evaluate the expression. $$\begin{array}{|c|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5 & 6 \\\\\hline f(x) & 2 & 3 & 5 & 1 & 6 & 3 \\\\\hline g(x) & 3 & 5 & 6 & 2 & 1 & 4 \\\\\hline\end{array}$$ $$(f \circ f)(5)$$