1. Rakesha claims that the equation f(n) = 5n – 7 is the function notation for the sequence that is represented by the explicit formula a, = -2 + 5(n – 1). James doesn't understand how this can be the case. a. Help James by listing the steps to write the explicit formula of the given sequence in function notation. Provide a rationale for each step. b. Graph the function. Label the first 5 values of the sequence on the graph.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.3: Geometric Sequences
Problem 52SE: Use explicit formulas to give two examples of geometric sequences whose 7thterms are 1024.
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1. Rakesha claims that the equation f(n) = 5n – 7 is the function notation for the sequence that is
represented by the explicit formula a, = -2 + 5(n – 1). James doesn't understand how this can be
the case.
a. Help James by listing the steps to write the explicit formula of the given sequence in function
notation. Provide a rationale for each step.
b. Graph the function. Label the first 5 values of the sequence on the graph.
2. Determine whether each table of values represents a linear function. For those that represent
linear functions, write the function. For those that do not, explain why not.
a.
b.
C.
f(x)
f(x)
f(x)
3.
14
2
1
11
4
18
1
-1
16
5
23
2
-4
3
21
6
29
3
-7
26
3. Calculate the average rate of change for each linear function using the formula. Show your work.
а.
b.
AY
f(x)
3
-4
7
4.
9
8
12
14
4.
Transcribed Image Text:Practice 1. Rakesha claims that the equation f(n) = 5n – 7 is the function notation for the sequence that is represented by the explicit formula a, = -2 + 5(n – 1). James doesn't understand how this can be the case. a. Help James by listing the steps to write the explicit formula of the given sequence in function notation. Provide a rationale for each step. b. Graph the function. Label the first 5 values of the sequence on the graph. 2. Determine whether each table of values represents a linear function. For those that represent linear functions, write the function. For those that do not, explain why not. a. b. C. f(x) f(x) f(x) 3. 14 2 1 11 4 18 1 -1 16 5 23 2 -4 3 21 6 29 3 -7 26 3. Calculate the average rate of change for each linear function using the formula. Show your work. а. b. AY f(x) 3 -4 7 4. 9 8 12 14 4.
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