6. Write the algebraic definition for the piecewise function graph. y=x+2 -5-4-3-2-1 5 4 3- 2 + + 2 3 4 5 y=-x+2 2 32 y=0 4 5 X
6. Write the algebraic definition for the piecewise function graph. y=x+2 -5-4-3-2-1 5 4 3- 2 + + 2 3 4 5 y=-x+2 2 32 y=0 4 5 X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Write the algebraic definition for the
![### Algebraic Definition for a Piecewise Function
**Problem 6:** Write the algebraic definition for the piecewise function graph.
#### Graph Explanation
The graph shows a piecewise function defined by three different equations over specified intervals:
1. **Line Segment 1:** \( y = x + 2 \)
- This line rises with a slope of 1 and a y-intercept at 2.
- It is defined over the interval \(-2 \leq x < 0\).
2. **Line Segment 2:** \( y = -x + 2 \)
- This line descends with a slope of -1 and has a y-intercept at 2.
- It is defined over the interval \(0 \leq x < 2\).
3. **Line Segment 3:** \( y = 0 \)
- This is a horizontal line at y = 0.
- It is defined over the interval \(2 \leq x < 5\).
#### Function Definition
The piecewise function \( f(x) \) can be expressed as follows:
\[ f(x) =
\begin{cases}
x + 2 & \text{for } -2 \leq x < 0 \\
-x + 2 & \text{for } 0 \leq x < 2 \\
0 & \text{for } 2 \leq x < 5
\end{cases}
\]
#### Answer Choices
a. 0
b. \(-x + 2\)
c. \(x + 2\)
d. \(-2 \leq x < 0\)
e. \(0 \leq x < 2\)
f. \(2 \leq x < 5\)
g. \(-2\)
h. 2
i. \(-x - 2\)
This exercise requires identifying and selecting the correct algebraic expressions and intervals to correctly write the piecewise function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe209da98-9d2a-41c6-b4dc-35971da8393b%2Fef4c1e05-c4c1-4098-8100-7652f40ea42b%2Fovqlq2_processed.png&w=3840&q=75)
Transcribed Image Text:### Algebraic Definition for a Piecewise Function
**Problem 6:** Write the algebraic definition for the piecewise function graph.
#### Graph Explanation
The graph shows a piecewise function defined by three different equations over specified intervals:
1. **Line Segment 1:** \( y = x + 2 \)
- This line rises with a slope of 1 and a y-intercept at 2.
- It is defined over the interval \(-2 \leq x < 0\).
2. **Line Segment 2:** \( y = -x + 2 \)
- This line descends with a slope of -1 and has a y-intercept at 2.
- It is defined over the interval \(0 \leq x < 2\).
3. **Line Segment 3:** \( y = 0 \)
- This is a horizontal line at y = 0.
- It is defined over the interval \(2 \leq x < 5\).
#### Function Definition
The piecewise function \( f(x) \) can be expressed as follows:
\[ f(x) =
\begin{cases}
x + 2 & \text{for } -2 \leq x < 0 \\
-x + 2 & \text{for } 0 \leq x < 2 \\
0 & \text{for } 2 \leq x < 5
\end{cases}
\]
#### Answer Choices
a. 0
b. \(-x + 2\)
c. \(x + 2\)
d. \(-2 \leq x < 0\)
e. \(0 \leq x < 2\)
f. \(2 \leq x < 5\)
g. \(-2\)
h. 2
i. \(-x - 2\)
This exercise requires identifying and selecting the correct algebraic expressions and intervals to correctly write the piecewise function.
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