### Understanding Function ChangesA function is given:\[ f(x) = 4x - 7 \]Two values are provided for the variable $ x $:\[ x = 2 \]\[ x = 3 \]#### Step-by-Step Instructions:1. **Determine the Net Change (a):** Calculate the difference in the function's value between the two given $ x $-values. \[ \Delta f = f(x_2) - f(x_1) \] Where: - $ x_1 = 2 $ - $ x_2 = 3 $ Using these values, find $ f(2) $ and $ f(3) $. Input your result in the provided box. \[ \boxed{} \]2. **Determine the Average Rate of Change (b):** Calculate the average rate of change of the function between the given $ x $-values. This is akin to finding the slope of the line that connects the points $(2, f(2))$ and $(3, f(3))$. The formula is: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] Again, using the values $ x_1 = 2 $ and $ x_2 = 3 $, calculate the result. Input your result in the provided box. \[ \boxed{} \]**Example Calculation Steps:**1. **Find $ f(2) $ and $ f(3) $**: \[ f(2) = 4(2) - 7 = 8 - 7 = 1 \] \[ f(3) = 4(3) - 7 = 12 - 7 = 5 \]2. **Calculate the Net Change**: \[ \Delta f = f(3) - f(2) = 5 - 1 = 4 \]3. **Calculate the Average Rate of Change**: \[ \text{Average Rate of Change} = \frac{\Delta f}{x_2 - x_1} = \frac{4}{3

Explanation of the answer is as follows

A function is given. fx) = 4x - 7; x= 2, x = 3 (a) Determine the net change between the given values of the variable. (b) Determine the average rate of change between the given values of the variable.

A function is given. fx) = 4x - 7; x= 2, x = 3 (a) Determine the net change between the given values of the variable. (b) Determine the average rate of change between the given values of the variable.

Algebra and Trigonometry (6th Edition)

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Author:Robert F. Blitzer

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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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Question

### Understanding Function Changes

A function is given:

\[ f(x) = 4x - 7 \]

Two values are provided for the variable $ x $:

\[ x = 2 \]
\[ x = 3 \]

#### Step-by-Step Instructions:

1. **Determine the Net Change (a):**
Calculate the difference in the function's value between the two given $ x $-values.

\[
\Delta f = f(x_2) - f(x_1)
\]

Where:
- $ x_1 = 2 $
- $ x_2 = 3 $

Using these values, find $ f(2) $ and $ f(3) $.

Input your result in the provided box.

\[
\boxed{}
\]

2. **Determine the Average Rate of Change (b):**
Calculate the average rate of change of the function between the given $ x $-values. This is akin to finding the slope of the line that connects the points $(2, f(2))$ and $(3, f(3))$.

The formula is:

\[
\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]

Again, using the values $ x_1 = 2 $ and $ x_2 = 3 $, calculate the result.

Input your result in the provided box.

\[
\boxed{}
\]

**Example Calculation Steps:**

1. **Find $ f(2) $ and $ f(3) $**:
\[
f(2) = 4(2) - 7 = 8 - 7 = 1
\]
\[
f(3) = 4(3) - 7 = 12 - 7 = 5
\]

2. **Calculate the Net Change**:
\[
\Delta f = f(3) - f(2) = 5 - 1 = 4
\]

3. **Calculate the Average Rate of Change**:
\[
\text{Average Rate of Change} = \frac{\Delta f}{x_2 - x_1} = \frac{4}{3

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