Chapter 2

What is the average rate of change of a function?

If you are given a function's equation, how do you determine if the function is even, odd, or neither?

If you are given a function's graph, how do you determine if the function is even, odd, or neither?

Write a function defined by an equation in \(x\) whose domain is \([-6, \infty)\)

What is a step function? Give an example of an everyday situation that can be modeled using such a function. Do not use the cost-of-mail example.

Give an example of an equation that does not define \(y\) as a function of \(x\) but that does define \(x\) as a function of \(y .\)

Explain how to find int \((-3.000004).\)

If \(f(x)=a x^{2}+b x+c\) and \(r_{1}=\frac{-b+\sqrt{b^{2}-4 a c}}{2 a}\) find \(f\left(r_{1}\right)\) without doing any algebra and explain how you arrived at your result.

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 TRACE coordinates of the minimum point on the graph of the function. What does this mean?

Almanacs, newspapers, magazines, and the Internet contain bar graphs and line graphs that describe how things are changing over time. For example, the graphs in Exercises \(79-82\) show how various phenomena are changing over time. Find a bar or line graph showing yearly changes that you find intriguing. Describe to the group what interests you about this data. The group should select their two favorite graphs. For each graph selected: a. Rewrite the data so that they are presented as a relation in the form of a set of ordered pairs. b. Determine whether the relation in part (a) is a function. Explain why the relation is a function, or why it is not.

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. $$f(x)=x^{3}-6 x^{2}+9 x+1$$

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. $$g(x)=\left|4-x^{2}\right|$$

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. $$h(x)=|x-2|+|x+2|$$

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. $$f(x)=x^{1 / 3}(x-4)$$

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

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. $$h(x)=2-x^{2 / 5}$$