## Practice1. **Rakesha claims that the equation $ f(n) = 5n - 7 $ is the function notation for the sequence that is represented by the explicit formula $ a_n = -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. \[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline 3 & 14 \\ 4 & 18 \\ 5 & 23 \\ 6 & 29 \\ \hline \end{array} \] b. \[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline 0 & 2 \\ 1 & -1 \\ 2 & -4 \\ 3 & -7 \\ \hline \end{array} \] c. \[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline 1 & 11 \\ 2 & 16 \\ 3 & 21 \\ 4 & 26 \\ \hline \end{array} \]3. **Calculate the average rate of change for each linear function using the formula. Show your work.** a. \[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline 3 & -4 \\ 7 & 4 \\ 9 & 8 \\ 12 & 14 \\ \hline

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Description: ## Practice1. **Rakesha claims that the equation $ f(n) = 5n - 7 $ is the function notation for the sequence that is represented by the explicit formula $ a_n = -2 + 5(n - 1) $. James doesn’t understand how this can be the case.** a. **Help

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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.

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

Topic Video

Question

## 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_n = -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.
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
3 & 14 \\
4 & 18 \\
5 & 23 \\
6 & 29 \\
\hline
\end{array}
\]

b.
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & 2 \\
1 & -1 \\
2 & -4 \\
3 & -7 \\
\hline
\end{array}
\]

c.
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
1 & 11 \\
2 & 16 \\
3 & 21 \\
4 & 26 \\
\hline
\end{array}
\]

3. **Calculate the average rate of change for each linear function using the formula. Show your work.**

a.
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
3 & -4 \\
7 & 4 \\
9 & 8 \\
12 & 14 \\
\hline

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