Based on the graph above, estimate (to one decimal place) the average rate of change from x=1 to x=3 **Problem: Average Rate of Change**The graph shown above features a function plotted on a coordinate plane. The x-axis ranges from -1 to 5, whereas the y-axis ranges from -1 to 6. The general shape of the function shows oscillation with several peak and trough points throughout the interval.Key points to note from the graph:- At $ x = 1 $, the function value $ y $ is approximately 2.- At $ x = 3 $, the function value $ y $ is approximately 1.**Question:**Based on the graph above, estimate (to one decimal place) the average rate of change from $ x = 1 $ to $ x = 3 $.**Solution:**To find the average rate of change from $ x = 1 $ to $ x = 3 $, we use the formula for the average rate of change of a function $ f $ over the interval from $ x = a $ to $ x = b $:\[ \text{Average rate of change} = \frac{f(b) - f(a)}{b - a} \]Here, $ a = 1 $ and $ b = 3 $.From the graph:- $ f(1) \approx 2 $- $ f(3) \approx 1 $Substitute these values into the formula:\[ \text{Average rate of change} = \frac{1 - 2}{3 - 1} = \frac{-1}{2} = -0.5 \]Therefore, the average rate of change from $ x = 1 $ to $ x = 3 $ is approximately $-0.5$.**Answer:**\[\boxed{-0.5}\] ### Detailed Explanation of the Graph#### Overview:The image features an "Enlarged Graph" window showing a continuous function plotted on a Cartesian plane. The graph has several key features, including peaks, troughs, and points of inflection, that can help us understand the behavior of the function.#### Axis Information:- **Horizontal Axis (X-Axis)**: The x-values range from 0 to 5.- **Vertical Axis (Y-Axis)**: The y-values range from -1 to 6.#### Key Features:1. **Starting Point (Approximate)**: - At $ x = 0 $, the graph starts at approximately $ y = 1 $. 2. **First Peak**: - The graph rises and reaches a local maximum slightly before $ x = 1 $, approximately at $ y = 3.5 $.3. **First Trough**: - After the first peak, the graph descends to a local minimum at $ x \approx 1.5 $ and $ y \approx 2 $.4. **Global Maximum**: - The graph then ascends again to reach a global maximum at $ x \approx 2.5 $ and $ y = 6 $.5. **Second Trough**: - The function falls to another local minimum at approximately $ x = 3.8 $, with $ y $ dropping close to $ y = 0 $.6. **Third Peak**: - The graph then rises to a smaller peak around $ x = 4.3 $ with $ y \approx 1.5 $.7. **Ending Point**: - The graph finally declines and approaches $ x = 5 $ and $ y \approx 0 $.#### Analysis:The function displayed seems to be a complex polynomial or a trigonometric function given its multiple peaks and troughs. Each change in direction suggests points where derivatives or changes in the slope would be significant for deeper calculus-based analyses, such as finding the points of inflection or calculating the function's derivative.#### Educational Usage:- **Curve Analysis**: This graph can be useful to teach students about local maxima and minima, as well as global extremum points.- **Derivative Application**: Students can derive the function and apply it in finding exact critical points.- **Integration**: By integrating the function over

Answered: Image /qna-images/answer/8b0593e2-d9ac-4da3-b09f-8c43d8d38d6f.jpg

Answered: 5 2 3 Based on the graph above,…

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5 2 3 Based on the graph above, estimate (to one decimal place) the average rate of change from æ = 1 to x = 3. 2.

Algebra and Trigonometry (6th Edition)

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ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

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

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Based on the graph above, estimate (to one decimal place) the average rate of change from x=1 to x=3

**Problem: Average Rate of Change**

The graph shown above features a function plotted on a coordinate plane. The x-axis ranges from -1 to 5, whereas the y-axis ranges from -1 to 6. The general shape of the function shows oscillation with several peak and trough points throughout the interval.

Key points to note from the graph:
- At $ x = 1 $, the function value $ y $ is approximately 2.
- At $ x = 3 $, the function value $ y $ is approximately 1.

**Question:**
Based on the graph above, estimate (to one decimal place) the average rate of change from $ x = 1 $ to $ x = 3 $.

**Solution:**
To find the average rate of change from $ x = 1 $ to $ x = 3 $, we use the formula for the average rate of change of a function $ f $ over the interval from $ x = a $ to $ x = b $:

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

Here, $ a = 1 $ and $ b = 3 $.

From the graph:
- $ f(1) \approx 2 $
- $ f(3) \approx 1 $

Substitute these values into the formula:

\[ \text{Average rate of change} = \frac{1 - 2}{3 - 1} = \frac{-1}{2} = -0.5 \]

Therefore, the average rate of change from $ x = 1 $ to $ x = 3 $ is approximately $-0.5$.

**Answer:**
\[
\boxed{-0.5}
\]

### Detailed Explanation of the Graph

#### Overview:

The image features an "Enlarged Graph" window showing a continuous function plotted on a Cartesian plane. The graph has several key features, including peaks, troughs, and points of inflection, that can help us understand the behavior of the function.

#### Axis Information:
- **Horizontal Axis (X-Axis)**: The x-values range from 0 to 5.
- **Vertical Axis (Y-Axis)**: The y-values range from -1 to 6.

#### Key Features:
1. **Starting Point (Approximate)**:
- At $ x = 0 $, the graph starts at approximately $ y = 1 $.

2. **First Peak**:
- The graph rises and reaches a local maximum slightly before $ x = 1 $, approximately at $ y = 3.5 $.

3. **First Trough**:
- After the first peak, the graph descends to a local minimum at $ x \approx 1.5 $ and $ y \approx 2 $.

4. **Global Maximum**:
- The graph then ascends again to reach a global maximum at $ x \approx 2.5 $ and $ y = 6 $.

5. **Second Trough**:
- The function falls to another local minimum at approximately $ x = 3.8 $, with $ y $ dropping close to $ y = 0 $.

6. **Third Peak**:
- The graph then rises to a smaller peak around $ x = 4.3 $ with $ y \approx 1.5 $.

7. **Ending Point**:
- The graph finally declines and approaches $ x = 5 $ and $ y \approx 0 $.

#### Analysis:
The function displayed seems to be a complex polynomial or a trigonometric function given its multiple peaks and troughs. Each change in direction suggests points where derivatives or changes in the slope would be significant for deeper calculus-based analyses, such as finding the points of inflection or calculating the function's derivative.

#### Educational Usage:
- **Curve Analysis**: This graph can be useful to teach students about local maxima and minima, as well as global extremum points.
- **Derivative Application**: Students can derive the function and apply it in finding exact critical points.
- **Integration**: By integrating the function over

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