Reading Questions for Sections 2.2 and 2.3

Name:______Reading Questions for Sections 2.2 and 2.3 Section 2.2 1. In example 3, page 70, analyze, piece by piece, what happens in the expression for the function h(t) by answering the following questions: a. What happens to the quantity (.9)t as t ® Ҙ ?

b. What happens to the denominator as t ® Ҙ ?

c. What happens to the entire fraction as t ® Ҙ ?

2. Often it’s helpful to consider what happens at the extremes of a situation. In problem 1, we looked at the extreme when t gets very big. Now consider the other extreme value of the function. a. What is the smallest value of t that is in the stated domain of the function?

b. What is the value of the function at this smallest value of t?

3. Looking at what happens at exceptional points in the domain of a function also helps us understand the overall behavior of the function. In example 4 on page 71, a. For what input value(s) is the function undefined?

b. What does the graph look like near the point(s) where the function is undefined?

c. Is the point where the function is undefined in the domain of the function?

d. What does the behavior near the undefined point tell you about the range of the function? Section 2.3 1. Consider the graph in the solution to example 2 at the bottom of page 75. Suppose there were two such graphs, one for the winner of the triathlon and one for the loser. a. Compare the domain and range of the graphs of the winner and loser.

b. Would it be possible for the slopes of all three line segments on the loser’s graph to be larger than the slopes of all three segments of the winner’s graph? (Explain.)

c. Would it be possible for any slope on the loser’s graph to be larger than the slope of the corresponding segment of the winner’s graph? (Explain.)