Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Transcription for Educational Website:**
---
**Graph the piecewise-defined function.**
\[ f(x) = \begin{cases}
-\frac{1}{2}x^2 + 5 & \text{for } x \leq 2 \\
\frac{1}{2}x & \text{for } x > 2
\end{cases} \]
---
**Choose the correct graph.**
- **Option A:** A graph with two segments. The first segment is a downward-opening parabola ending at \( x = 2 \). The second segment is a line with a positive slope starting after \( x = 2 \).
- **Option B:** A graph with two segments. The first segment is a line with a positive slope ending at \( x = 2 \). The second segment is a continuation of the line starting after \( x = 2 \).
- **Option C:** A graph with two segments. The first segment is a downward-opening parabola ending at \( x = 2 \). The second segment is a line with a negative slope starting after \( x = 2 \).
- **Option D:** A graph with two segments. The first segment is a downward-opening parabola that ends at \( x = 2 \). The second segment begins at \( x = 2 \), continues upward, and seems to have a slope of \( \frac{1}{2} \).
**Note:** Identify the graph that accurately represents the given piecewise function, considering where each part of the function applies based on the value of \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc43e03e1-b353-4d50-a726-bab1a8232fef%2F6345283c-68b7-485b-8b57-849888ce73c0%2F96zcexo_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
---
**Graph the piecewise-defined function.**
\[ f(x) = \begin{cases}
-\frac{1}{2}x^2 + 5 & \text{for } x \leq 2 \\
\frac{1}{2}x & \text{for } x > 2
\end{cases} \]
---
**Choose the correct graph.**
- **Option A:** A graph with two segments. The first segment is a downward-opening parabola ending at \( x = 2 \). The second segment is a line with a positive slope starting after \( x = 2 \).
- **Option B:** A graph with two segments. The first segment is a line with a positive slope ending at \( x = 2 \). The second segment is a continuation of the line starting after \( x = 2 \).
- **Option C:** A graph with two segments. The first segment is a downward-opening parabola ending at \( x = 2 \). The second segment is a line with a negative slope starting after \( x = 2 \).
- **Option D:** A graph with two segments. The first segment is a downward-opening parabola that ends at \( x = 2 \). The second segment begins at \( x = 2 \), continues upward, and seems to have a slope of \( \frac{1}{2} \).
**Note:** Identify the graph that accurately represents the given piecewise function, considering where each part of the function applies based on the value of \( x \).
Expert Solution
Step 1a
We have to find out
Step by step
Solved in 2 steps
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education