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
Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
![### Graphing Piecewise-Defined Functions
#### Problem Description
Graph the piecewise-defined function:
\[ f(x) = \begin{cases}
x - 1 & \text{if } x \leq -3 \\
-4 & \text{if } x > -3
\end{cases} \]
Choose the correct graph.
#### Available Graphs:
- **Option A**
- A graph with two distinct line segments.
- For \( x \leq -3 \), the graph shows a line with a slope of 1 starting from the point (-4, -5) and moving upward to the left.
- For \( x > -3 \), the graph shows a horizontal line at \( y = -4 \).
- **Option B**
- A graph with two line segments.
- For \( x \leq -3 \), the graph shows a line with a slope of 1 starting from the point (-4, -5) and moving upward to the right.
- For \( x > -3 \), the graph shows a horizontal line at \( y = -4 \).
- **Option C**
- A graph with two line segments.
- For \( x \leq -3 \), the graph shows a downward-sloping line starting at the point (-3, -4) moving left.
- No distinct horizontal segment for \( x > -3 \).
- **Option D**
- A graph with two line segments.
- For \( x \leq -3 \), the graph shows a line starting from an unspecified point and moving downward to the left.
- For \( x > -3 \), the graph shows a horizontal line at \( y = -4 \).
#### Explanation:
- The piecewise-defined function has two parts:
1. \( f(x) = x - 1 \) for \( x \leq -3 \). This defines a line with a slope of 1 and y-intercept of -4.
2. \( f(x) = -4 \) for \( x > -3 \). This defines a horizontal line at y = -4.
- To correctly choose the graph:
- For \( x \leq -3 \), the function should show an increasing line (slope = 1) that passes through \( x = -3 \).
- For \( x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89ef0769-2756-4878-bbe7-8a87b2840a03%2F89f37d1a-030a-4cf2-a986-9716098a36b3%2Fka1s2n_processed.png&w=3840&q=75)
Transcribed Image Text:### Graphing Piecewise-Defined Functions
#### Problem Description
Graph the piecewise-defined function:
\[ f(x) = \begin{cases}
x - 1 & \text{if } x \leq -3 \\
-4 & \text{if } x > -3
\end{cases} \]
Choose the correct graph.
#### Available Graphs:
- **Option A**
- A graph with two distinct line segments.
- For \( x \leq -3 \), the graph shows a line with a slope of 1 starting from the point (-4, -5) and moving upward to the left.
- For \( x > -3 \), the graph shows a horizontal line at \( y = -4 \).
- **Option B**
- A graph with two line segments.
- For \( x \leq -3 \), the graph shows a line with a slope of 1 starting from the point (-4, -5) and moving upward to the right.
- For \( x > -3 \), the graph shows a horizontal line at \( y = -4 \).
- **Option C**
- A graph with two line segments.
- For \( x \leq -3 \), the graph shows a downward-sloping line starting at the point (-3, -4) moving left.
- No distinct horizontal segment for \( x > -3 \).
- **Option D**
- A graph with two line segments.
- For \( x \leq -3 \), the graph shows a line starting from an unspecified point and moving downward to the left.
- For \( x > -3 \), the graph shows a horizontal line at \( y = -4 \).
#### Explanation:
- The piecewise-defined function has two parts:
1. \( f(x) = x - 1 \) for \( x \leq -3 \). This defines a line with a slope of 1 and y-intercept of -4.
2. \( f(x) = -4 \) for \( x > -3 \). This defines a horizontal line at y = -4.
- To correctly choose the graph:
- For \( x \leq -3 \), the function should show an increasing line (slope = 1) that passes through \( x = -3 \).
- For \( x
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.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