Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Functions
Section9.CR: Review Problem Set
Problem 24CR: An outpatient operating room charges each patient a fixed amount per surgery plus an amount per...
Related questions
Topic Video
Question
How do I sketch the function?
![### Piecewise Function and Its Graph
In this example, we are given a piecewise function \( f(x) \) defined as follows:
\[
f(x) =
\begin{cases}
-x - 6 & \text{if } x \leq -3 \\
-3 & \text{if } -3 < x \leq 4 \\
1.5 - 7 & \text{if } x > 4
\end{cases}
\]
We are required to sketch the graph of this piecewise function based on the given conditions.
### Analysis of Each Piece
1. **For \( x \leq -3 \):** The function is \( f(x) = -x - 6 \).
- This is a linear function with a negative slope.
- As \( x \) decreases, \( f(x) \) increases according to the equation.
2. **For \( -3 < x \leq 4 \):** The function is \( f(x) = -3 \).
- This is a constant function, meaning for all \( x \) in this interval, \( f(x) \) is always -3.
3. **For \( x > 4 \):** The function is \( f(x) = 1.5 - 7 \).
- This simplifies to \( f(x) = -5.5 \), indicating another constant function where \( f(x) \) is always -5.5 for \( x \) greater than 4.
### Graph Explanation
The provided graph paper has both horizontal and vertical axes marked with grid lines. Here's how to sketch the graph based on the piecewise function:
1. **For the interval \( x \leq -3 \):**
- Plot the line \( f(x) = -x - 6 \).
- For example, when \( x = -3 \), \( f(x) = -(-3) - 6 = 3 - 6 = -3 \).
- Extend the line with that slope to the left of \( x = -3 \).
2. **For the interval \( -3 < x \leq 4 \):**
- Draw a horizontal line at \( f(x) = -3 \)
- This extends from just greater than \( x = -3 \) to \( x = 4 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51d45a60-639a-4786-9439-9ee8ed3be594%2F7f0a89c3-a6cf-4474-b859-415b90e8a974%2Fpw39wev_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:### Piecewise Function and Its Graph
In this example, we are given a piecewise function \( f(x) \) defined as follows:
\[
f(x) =
\begin{cases}
-x - 6 & \text{if } x \leq -3 \\
-3 & \text{if } -3 < x \leq 4 \\
1.5 - 7 & \text{if } x > 4
\end{cases}
\]
We are required to sketch the graph of this piecewise function based on the given conditions.
### Analysis of Each Piece
1. **For \( x \leq -3 \):** The function is \( f(x) = -x - 6 \).
- This is a linear function with a negative slope.
- As \( x \) decreases, \( f(x) \) increases according to the equation.
2. **For \( -3 < x \leq 4 \):** The function is \( f(x) = -3 \).
- This is a constant function, meaning for all \( x \) in this interval, \( f(x) \) is always -3.
3. **For \( x > 4 \):** The function is \( f(x) = 1.5 - 7 \).
- This simplifies to \( f(x) = -5.5 \), indicating another constant function where \( f(x) \) is always -5.5 for \( x \) greater than 4.
### Graph Explanation
The provided graph paper has both horizontal and vertical axes marked with grid lines. Here's how to sketch the graph based on the piecewise function:
1. **For the interval \( x \leq -3 \):**
- Plot the line \( f(x) = -x - 6 \).
- For example, when \( x = -3 \), \( f(x) = -(-3) - 6 = 3 - 6 = -3 \).
- Extend the line with that slope to the left of \( x = -3 \).
2. **For the interval \( -3 < x \leq 4 \):**
- Draw a horizontal line at \( f(x) = -3 \)
- This extends from just greater than \( x = -3 \) to \( x = 4 \
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9781285195728/9781285195728_smallCoverImage.gif)
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9781285195728/9781285195728_smallCoverImage.gif)
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337278461/9781337278461_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Algebra for College Students](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning