Based on the graph above, estimate (to one decimal place) the average rate of change from x=1 to x=3 ### Graph Analysis and Calculation#### Graph Description:The graph presented is of an unknown function plotted on an x-y axis grid. The x-axis ranges from -1 to 5, while the y-axis ranges from -1 to 6. The function has multiple peaks and troughs, indicating several changes in direction.#### Specific Points and Shape:- At $ x = 0 $, the value of the function is slightly above 0.- The function increases sharply, reaching a peak between $ x = 1 $ and $ x = 2 $.- The function then decreases slightly and rises again to a higher peak between $ x = 2 $ and $ x = 3 $.- After this peak, the function decreases steeply, dipping below 1 before rising slightly again as $ x $ approaches 5.#### Question and Instructions:Based on the graph above, estimate (to one decimal place) the average rate of change from $ x = 1 $ to $ x = 3 $.##### Calculation:1. Identify the coordinates of the function at $ x = 1 $ and $ x = 3 $. - At $ x = 1 $, the function value (y-value) is approximately 4. - At $ x = 3 $, the function value is approximately 5.2. Use the formula for average rate of change: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] Where $ x_1 = 1 $ and $ x_2 = 3 $.3. Substitute the function values: \[ \text{Average Rate of Change} = \frac{5 - 4}{3 - 1} = \frac{1}{2} = 0.5 \]##### Input Box for Answer:- The average rate of change from $ x = 1 $ to $ x = 3 $ is $ 0.5 $. Please enter "0.5" in the provided box to complete your answer.---**Note:** This transcription includes a detailed description of the graph, steps to understand and calculate the average rate of change, and a conclusion to be entered by the student.

Answered: 4 2 3 Based on the graph above,…

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4 2 3 Based on the graph above, estimate (to one decimal place) the average rate of change from x = 1 to a = 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

### Graph Analysis and Calculation

#### Graph Description:
The graph presented is of an unknown function plotted on an x-y axis grid. The x-axis ranges from -1 to 5, while the y-axis ranges from -1 to 6. The function has multiple peaks and troughs, indicating several changes in direction.

#### Specific Points and Shape:
- At $ x = 0 $, the value of the function is slightly above 0.
- The function increases sharply, reaching a peak between $ x = 1 $ and $ x = 2 $.
- The function then decreases slightly and rises again to a higher peak between $ x = 2 $ and $ x = 3 $.
- After this peak, the function decreases steeply, dipping below 1 before rising slightly again as $ x $ approaches 5.

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

##### Calculation:
1. Identify the coordinates of the function at $ x = 1 $ and $ x = 3 $.
- At $ x = 1 $, the function value (y-value) is approximately 4.
- At $ x = 3 $, the function value is approximately 5.

2. Use the formula for average rate of change:
\[
\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]
Where $ x_1 = 1 $ and $ x_2 = 3 $.

3. Substitute the function values:
\[
\text{Average Rate of Change} = \frac{5 - 4}{3 - 1} = \frac{1}{2} = 0.5
\]

##### Input Box for Answer:
- The average rate of change from $ x = 1 $ to $ x = 3 $ is $ 0.5 $.
Please enter "0.5" in the provided box to complete your answer.

---
**Note:** This transcription includes a detailed description of the graph, steps to understand and calculate the average rate of change, and a conclusion to be entered by the student.

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