The graph of a function is given. (a) Determine the net change between the indicated points on the graph. (b) Determine the average rate of change between the indicated points on the graph.
The graph of a function is given. (a) Determine the net change between the indicated points on the graph. (b) Determine the average rate of change between the indicated points on the graph.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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![### Problem Description and Graph Explanation
**The graph of a function is given:**
- The graph provided is a curved function plotted on a coordinate grid.
- The x-axis ranges approximately from 0 to 6, and the y-axis ranges approximately from 0 to 6.
- Specific points on the graph are indicated, forming a curvature that peaks and then declines.
- A dashed line connects two specific points on the curve, with coordinates approximately at (1, 4) and (5, 2).
- The function starts at a higher y-value around x=0, rises to a peak near (3, 5), and then declines as x increases.
#### Questions
(a) Determine the net change between the indicated points on the graph.
**Answer:**
The net change is the difference in the y-values between the points (1, 4) and (5, 2).
\[ \text{Net change} = 2 - 4 = -2. \]
(b) Determine the average rate of change between the indicated points on the graph.
**Answer:**
The average rate of change is the change in the y-values divided by the change in the x-values between the points (1, 4) and (5, 2).
\[ \text{Average rate of change} = \frac{2 - 4}{5 - 1} = \frac{-2}{4} = -0.5. \]
### Diagrams and Their Explanation
**Graph:**
- The coordinate system displays a grid with labeled x and y axes.
- The function is plotted as a curved line starting low on the y-axis, increasing to a peak, and then decreasing again.
- The labeled points (1, 4) and (5, 2) are connected with a dashed line to indicate the interval for which calculations are requested.
This graph helps to visualize the function's behavior and aids in understanding the concepts of net change and average rate of change between two points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf307311-1e00-4fe9-8eeb-e087e581a37a%2Ff7e96ce4-940d-4655-861b-ead9c77c2e6e%2Fm2l7tj_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description and Graph Explanation
**The graph of a function is given:**
- The graph provided is a curved function plotted on a coordinate grid.
- The x-axis ranges approximately from 0 to 6, and the y-axis ranges approximately from 0 to 6.
- Specific points on the graph are indicated, forming a curvature that peaks and then declines.
- A dashed line connects two specific points on the curve, with coordinates approximately at (1, 4) and (5, 2).
- The function starts at a higher y-value around x=0, rises to a peak near (3, 5), and then declines as x increases.
#### Questions
(a) Determine the net change between the indicated points on the graph.
**Answer:**
The net change is the difference in the y-values between the points (1, 4) and (5, 2).
\[ \text{Net change} = 2 - 4 = -2. \]
(b) Determine the average rate of change between the indicated points on the graph.
**Answer:**
The average rate of change is the change in the y-values divided by the change in the x-values between the points (1, 4) and (5, 2).
\[ \text{Average rate of change} = \frac{2 - 4}{5 - 1} = \frac{-2}{4} = -0.5. \]
### Diagrams and Their Explanation
**Graph:**
- The coordinate system displays a grid with labeled x and y axes.
- The function is plotted as a curved line starting low on the y-axis, increasing to a peak, and then decreasing again.
- The labeled points (1, 4) and (5, 2) are connected with a dashed line to indicate the interval for which calculations are requested.
This graph helps to visualize the function's behavior and aids in understanding the concepts of net change and average rate of change between two points.
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