*23) Gketch the graph of f by hand and use r sketch to find the absolute and local maximdm and winimum valucs of f. your 2xナ 1 L4-2x f 1Ex <3 1f osX f(x) =
*23) Gketch the graph of f by hand and use r sketch to find the absolute and local maximdm and winimum valucs of f. your 2xナ 1 L4-2x f 1Ex <3 1f osX f(x) =
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section: Chapter Questions
Problem 8CC: What does it mean to say that f(4) is a local maximum valueof f ?
Related questions
Question
![**Exercise 28:**
Sketch the graph of \( f \) by hand and use your sketch to find the absolute and local maximum and minimum values of \( f \).
\[ f(x) =
\begin{cases}
2x + 1 & \text{if } 0 \leq x < 1 \\
4 - 2x & \text{if } 1 \leq x \leq 3
\end{cases}
\]
**Explanation of Graph:**
- The graph consists of two linear pieces defined within different intervals.
- For \( 0 \leq x < 1 \), the function is \( f(x) = 2x + 1 \). This is a line with a slope of 2 and a y-intercept at 1.
- For \( 1 \leq x \leq 3 \), the function is \( f(x) = 4 - 2x \). This is a line with a slope of -2 and a y-intercept at 4.
**Diagram Explanation:**
The graph starts with an upward sloping line segment from \( (0, 1) \) to just before \( (1, 3) \). At \( x = 1 \), the graph switches to a downward sloping line starting from \( (1, 2) \) to \( (3, -2) \). The intersection of these two segments at \( x = 1 \) represents a transition from the first linear expression to the second one.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dcb78da-3870-4da6-8da3-7759b1e48992%2F3a61cc8b-ca50-4bc1-9065-1b2c7419a61d%2F81mknhr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 28:**
Sketch the graph of \( f \) by hand and use your sketch to find the absolute and local maximum and minimum values of \( f \).
\[ f(x) =
\begin{cases}
2x + 1 & \text{if } 0 \leq x < 1 \\
4 - 2x & \text{if } 1 \leq x \leq 3
\end{cases}
\]
**Explanation of Graph:**
- The graph consists of two linear pieces defined within different intervals.
- For \( 0 \leq x < 1 \), the function is \( f(x) = 2x + 1 \). This is a line with a slope of 2 and a y-intercept at 1.
- For \( 1 \leq x \leq 3 \), the function is \( f(x) = 4 - 2x \). This is a line with a slope of -2 and a y-intercept at 4.
**Diagram Explanation:**
The graph starts with an upward sloping line segment from \( (0, 1) \) to just before \( (1, 3) \). At \( x = 1 \), the graph switches to a downward sloping line starting from \( (1, 2) \) to \( (3, -2) \). The intersection of these two segments at \( x = 1 \) represents a transition from the first linear expression to the second one.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
