Throughout this chapter, you have been learning about sequences. In Chapter 1, you started to learn about functions. But what is the

difference? In this lesson, you will compare and contrast sequences with functions. By the end of the lesson, you will be

able to answer these questions:Is a sequence different from a function?

What is the difference between a sequence t(n) and the function f(x) with the same equation?

5-111. Consider sequence t(n) below.

−5, −1, 3, 7, … a) Create multiple representations, namely, a table, a graph

and an equation (recursive or explicit), for the sequence t(n).b) Is it possible for the equation representing t(n) to equal

400? Justify your answer.c) Create the same multiple representations as you did in part

(a) for the function f(x) = 4x − 9. How are f(x) and t(n) different? How can you see their differences in each of the representations?

d) For the function f(x) = 4x − 9, is it possible for f(x) to equal 400? Explain why or why not.

5-112. Let us consider the difference between t(n) = 2 · 3n and f(x) = 2 · 3x .

a) Is f(x) = 2 · 3x a function? Why or why not? Is t(n) = 2 · 3n a function?

b) Is it possible for t(n) to equal 1400? If so, find the value of n that makes t(n) = 1400. If not, justify why not.

c) Is it possible for f(x) to equal 1400? If so, find the value of x that makes f(x) = 1400. Be prepared to share your solving strategy with the class.

d) How are the two functions similar? How are they different?

5-113. LEARNING LOG

• Is a sequence a function? Justify your answer completely. If so, what makes it different from the functions that are usually written in the form f(x) = ________? If not, why not? Be prepared to share your ideas with the class. After a class discussion about these questions, answer the questions in your Learning Log. Title this entry “Sequences vs. Functions” and label it with today’s date.

5-114

• Janine was working on her homework but lost part of it. She knew that one output of p(r) = 2 · 5 r is 78,000, but she could not remember if p(r) is a sequence or if it's a regular function. With your team, help her figure it out. Be sure to justify your decision.

5-115

• Khalil is working with a geometric sequence. He knows that t(0) = 3 and that the sum of the first three terms (t(0) , t(1) , and t(2) ) is 63. Help him figure out the sequence. Be prepared to share your strategies with the class.

5-116. Additional Challenge: Discuss with your team how you can use your graphing calculator to solve each of the following equations for x, accurate to the nearest

0.01.a) 200(0.5)x = 3.125

b) 318 = 6 · 3x