Find the symbolic form of the piecewise function show below. Make certain to show appropriate work beyond just guessing and checking in Desmos (e.g., slope calculations, etc.).
Find the symbolic form of the piecewise function show below. Make certain to show appropriate work beyond just guessing and checking in Desmos (e.g., slope calculations, etc.).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
need help answering the image below.
![**Instructions:**
Find the symbolic form of the piecewise function shown below. Make certain to show appropriate work beyond just guessing and checking in Desmos (e.g., slope calculations, etc.).
**Graph Explanation:**
The graph consists of two line segments:
1. **First Line Segment:**
- Begins at the point (0, 4) and ends at (2, -2).
- The slope (m) can be calculated as:
\[
m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{-2 - 4}}{{2 - 0}} = \frac{{-6}}{2} = -3
\]
- Therefore, the equation of this line is \(y = -3x + 4\).
2. **Second Line Segment:**
- Begins at the point (2, -2) and ends at (8, 4).
- The slope (m) is:
\[
m = \frac{{4 - (-2)}}{{8 - 2}} = \frac{6}{6} = 1
\]
- Therefore, the equation of this line is \(y = x - 4\).
**Piecewise Function:**
The piecewise function can be described as:
\[
f(x) =
\begin{cases}
-3x + 4 & \text{for } 0 \leq x < 2 \\
x - 4 & \text{for } 2 \leq x \leq 8
\end{cases}
\]
The points at x = 0, x = 2, and x = 8 are carefully marked on the graph. Note the open circle at (2, -2) indicating the endpoint of the first line and closed circle indicating the start of the second line at that point.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd627bc06-52c0-4d11-87e8-f3ff50368dcf%2F63efcc3c-9758-4ef8-a8ea-e64c62f9e2ab%2Fjmtdvjg_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions:**
Find the symbolic form of the piecewise function shown below. Make certain to show appropriate work beyond just guessing and checking in Desmos (e.g., slope calculations, etc.).
**Graph Explanation:**
The graph consists of two line segments:
1. **First Line Segment:**
- Begins at the point (0, 4) and ends at (2, -2).
- The slope (m) can be calculated as:
\[
m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{-2 - 4}}{{2 - 0}} = \frac{{-6}}{2} = -3
\]
- Therefore, the equation of this line is \(y = -3x + 4\).
2. **Second Line Segment:**
- Begins at the point (2, -2) and ends at (8, 4).
- The slope (m) is:
\[
m = \frac{{4 - (-2)}}{{8 - 2}} = \frac{6}{6} = 1
\]
- Therefore, the equation of this line is \(y = x - 4\).
**Piecewise Function:**
The piecewise function can be described as:
\[
f(x) =
\begin{cases}
-3x + 4 & \text{for } 0 \leq x < 2 \\
x - 4 & \text{for } 2 \leq x \leq 8
\end{cases}
\]
The points at x = 0, x = 2, and x = 8 are carefully marked on the graph. Note the open circle at (2, -2) indicating the endpoint of the first line and closed circle indicating the start of the second line at that point.
Expert Solution
Step 1: Given Information:
Given that the graph of the piecewise function is:
. 
.
To find the symbolic form of the given piecewise function.
Step by step
Solved in 3 steps with 13 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
