I need help with this I sent a picture thank you # Educational Content: Average Rate of Change## Problem StatementIn this exercise, you are tasked with analyzing two functions, \( f(x) \) and \( g(x) \), to determine which function has the greater average rate of change over a specified interval. Below is the detailed explanation and description of the functions involved.### Functions1. **Function \( f(x) \):** \[ f(x) = x^2 + 3x \]2. **Function \( g(x) \):** values are given in a table:| \( x \) | \( g(x) \) ||---------|----------|| 0 | -3 || 2 | 4 || 3 | 11 || 5 | 24 || 6 | 36 || 8 | 43 || 10 | 46 |### TaskYou are asked to calculate the average rate of change for both functions over the interval \([2, 6]\) and determine which has the greater rate of change. Be sure to show your reasoning and calculations, as answers without supporting work will receive partial credit only.### How to Calculate Average Rate of ChangeThe average rate of change of a function over an interval \([a, b]\) is given by the formula:\[\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}\]Apply this formula to both functions over the specified interval:#### For \( f(x) \):- Calculate \( f(6) \) and \( f(2) \)- Substitute into the formula#### For \( g(x) \):- Use the table values \( g(6) \) and \( g(2) \)- Substitute into the same formula### ConclusionDetermine which function, \( f(x) \) or \( g(x) \), has the larger average rate of change based on your calculations. Provide a clear and concise explanation to support your findings. **Part III Questions:**Answer all questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps and explain your reasoning. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.**12. Two functions, \( f(x) \) and \( g(x) \), are given below. Determine which of these functions has the greater average rate of change over the interval \( 2 \leq x \leq 6 \). Support your final answer.**- \( f(x) = x^2 + 3x \)A table for \( g(x) \) is provided as follows:\[\begin{array}{|c|c|}\hlinex & g(x) \\\hline-3 & 2 \\0 & 3 \\2 & 5 \\3 & 6 \\5 & 8 \\6 & 10 \\8 & 11 \\10 & 12 \\\hline\end{array}\]**Explanation of the Diagram:**The diagram likely includes two parts: a depiction of a function and a note indicating “function over” with a rough sketch possibly highlighting a parabolic curve with annotations crossing out and correcting a drawn feature.

Answered: Image /qna-images/answer/0b69a21e-5a85-4df0-8740-dd64c6ecb5a3.jpg

Answered: Il. ILMOUTS 12. Two functions, f (x)…

Il. ILMOUTS 12. Two functions, f (x) and g(x), are given below. Determine which of these functions has the rate of change over the interval 2 < x <6. Support your final answer. f (x)= x² + 3x

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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I need help with this I sent a picture thank you

# Educational Content: Average Rate of Change

## Problem Statement

In this exercise, you are tasked with analyzing two functions, \( f(x) \) and \( g(x) \), to determine which function has the greater average rate of change over a specified interval. Below is the detailed explanation and description of the functions involved.

### Functions

1. **Function \( f(x) \):**
\[
f(x) = x^2 + 3x
\]

2. **Function \( g(x) \):** values are given in a table:

| \( x \) | \( g(x) \) |
|---------|----------|
| 0 | -3 |
| 2 | 4 |
| 3 | 11 |
| 5 | 24 |
| 6 | 36 |
| 8 | 43 |
| 10 | 46 |

### Task

You are asked to calculate the average rate of change for both functions over the interval \([2, 6]\) and determine which has the greater rate of change. Be sure to show your reasoning and calculations, as answers without supporting work will receive partial credit only.

### How to Calculate Average Rate of Change

The average rate of change of a function over an interval \([a, b]\) is given by the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

Apply this formula to both functions over the specified interval:

#### For \( f(x) \):

- Calculate \( f(6) \) and \( f(2) \)
- Substitute into the formula

#### For \( g(x) \):

- Use the table values \( g(6) \) and \( g(2) \)
- Substitute into the same formula

### Conclusion

Determine which function, \( f(x) \) or \( g(x) \), has the larger average rate of change based on your calculations. Provide a clear and concise explanation to support your findings.

**Part III Questions:**

Answer all questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps and explain your reasoning. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

**12. Two functions, \( f(x) \) and \( g(x) \), are given below. Determine which of these functions has the greater average rate of change over the interval \( 2 \leq x \leq 6 \). Support your final answer.**

- \( f(x) = x^2 + 3x \)

A table for \( g(x) \) is provided as follows:

\[
\begin{array}{|c|c|}
\hline
x & g(x) \\
\hline
-3 & 2 \\
0 & 3 \\
2 & 5 \\
3 & 6 \\
5 & 8 \\
6 & 10 \\
8 & 11 \\
10 & 12 \\
\hline
\end{array}
\]

**Explanation of the Diagram:**

The diagram likely includes two parts: a depiction of a function and a note indicating “function over” with a rough sketch possibly highlighting a parabolic curve with annotations crossing out and correcting a drawn feature.

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