Find the net signed area of ƒ (x) = x - 2 over the interval [0, 6], illustrated in the following image. YA -2 4 f(x)=x-2 2 A₂ A₁ 4 6 X

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
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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...
Question
**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.
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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