91Ó°ÊÓ

For each given function \(f(x),\) find two functions \(g(x)\) and \(h(x)\) such that \(f=h \circ g .\) Answers may vary. $$f(x)=(x-2)^{3}$$

For each given function \(f(x),\) find two functions \(g(x)\) and \(h(x)\) such that \(f=h \circ g .\) Answers may vary. $$f(x)=\sqrt{x+5}$$

Use the minimum and maximum features of a graphing calculator to find the intervals on which each function is increasing or decreasing. Round approximate answers to two decimal places. $$y=3 x^{2}-5 x-4$$

Determine algebraically whether the function is even, odd, or neither. Discuss the symmetry of each function. $$f(x)=1+\frac{1}{x^{2}}$$

Galdino drove his truck from 8 A.M. to 11 A.M. in the rain. From 11 A.M. to 4 P.M. the skies were clear and he averaged 5 mph more than he did in the rain. If the total distance traveled was 425 miles, then what was his average speed in the rain?

Let \(f(x)=3 x^{2}-x\) and \(g(x)=4 x-2 .\) Find the following. $$f(x+h)-f(x)$$

Let \(f(x)=3 x^{2}-x\) and \(g(x)=4 x-2 .\) Find the following. $$g(x+h)-g(x)$$

Determine the symmetry of the graph of the function \(f(x)=x^{3}-8 x\).

Use the minimum and maximum features of a graphing calculator to find the intervals on which each function is increasing or decreasing. Round approximate answers to two decimal places. $$y=-6 x^{2}+2 x-9$$

Determine algebraically whether the function is even, odd, or neither. Discuss the symmetry of each function. $$f(x)=\left(x^{2}-2\right)^{3}$$