Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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![**Checkpoint 1.9**
Find the net signed area of \( f(x) = x - 2 \) over the interval \([0, 6]\), illustrated in the following image.
![Graph detailing the function](https://www.example.com/image-link)
*Explanation of the Graph:*
The graph shows the function \( f(x) = x - 2 \) plotted on a coordinate plane.
- The function is a straight line with a slope of 1 and a y-intercept of -2.
- There are two distinct areas labeled \( A_1 \) and \( A_2 \).
Key observations from the graph:
- \( A_1 \) denotes the area above the x-axis from the interval where the function is positive.
- \( A_2 \) denotes the area below the x-axis from the interval where the function is negative.
The challenge is to compute the net signed area, which involves calculating the areas \( A_1 \) and \( A_2 \), then considering the appropriate signs for each segment based on their position relative to the x-axis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11c3e735-47a2-4be2-bcf0-76944b0744ea%2Fc43c216d-b36a-43b8-acc2-63ce95c750eb%2F8usmbum_processed.png&w=3840&q=75)
Transcribed Image Text:**Checkpoint 1.9**
Find the net signed area of \( f(x) = x - 2 \) over the interval \([0, 6]\), illustrated in the following image.
![Graph detailing the function](https://www.example.com/image-link)
*Explanation of the Graph:*
The graph shows the function \( f(x) = x - 2 \) plotted on a coordinate plane.
- The function is a straight line with a slope of 1 and a y-intercept of -2.
- There are two distinct areas labeled \( A_1 \) and \( A_2 \).
Key observations from the graph:
- \( A_1 \) denotes the area above the x-axis from the interval where the function is positive.
- \( A_2 \) denotes the area below the x-axis from the interval where the function is negative.
The challenge is to compute the net signed area, which involves calculating the areas \( A_1 \) and \( A_2 \), then considering the appropriate signs for each segment based on their position relative to the x-axis.
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