91Ó°ÊÓ

Explain how to find the difference quotient of a function \(f\) \(\frac{f(x+h)-f(x)}{h},\) if an equation for \(f\) is given.

Solve for \(y: \quad x=\frac{5}{y}+4\)

$$\text { Solve for } y: \quad x=y^{2}-1, y \geq 0$$

The function $$f(x)=-0.00002 x^{3}+0.008 x^{2}-0.3 x+6.95$$ models the number of annual physician visits, \(f(x),\) by a person of age \(x .\) Graph the function in a \([0,100,5]\) by \([0,40,2]\) viewing rectangle. What does the shape of the graph indicate about the relationship between one's age and the number of annual physician visits? Use the \([\mathrm{TABLE}]\) or minimum function capability to find the coordinates of the minimum point on the graph of the function. What does this mean?

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by \([-5,5,1]\) viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{3}-6 x^{2}+9 x+1$$

If \(f(x)=3 x+7,\) find \(\frac{f(a+h)-f(a)}{h}\)

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by \([-5,5,1]\) viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$g(x)=\left|4-x^{2}\right|$$

Give an example of a relation with the following characteristics: The relation is a function containing two ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function.

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by \([-5,5,1]\) viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$h(x)=|x-2|+|x+2|$$

What must be done to a function's equation so that its graph is shifted vertically upward?