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
I need help with 1& 2 pl
![**Title: Understanding Piecewise Functions**
**Introduction:**
This section explores the concept of piecewise functions through a specific example.
**Function Definition:**
The function \( f(x) \) is defined as a piecewise function:
\[
f(x) =
\begin{cases}
2, & \text{if } x > -3 \\
-2, & \text{if } x \leq -3
\end{cases}
\]
**Graph Explanation:**
The accompanying graph is a coordinate plane with both x and y axes ranging from -10 to 10.
- **For \( x > -3 \):** The function \( f(x) \) evaluates to 2. This is represented by a horizontal line at \( y = 2 \) for all \( x \) greater than -3. This portion of the graph will be an open circle at \( x = -3 \) on the line \( y = 2 \), extending to the right.
- **For \( x \leq -3 \):** The function \( f(x) \) evaluates to -2. This is represented by a horizontal line at \( y = -2 \) for all \( x \) less than or equal to -3. This portion will have a closed circle at \( x = -3 \) on the line \( y = -2 \), extending to the left.
The graph visually distinguishes the two conditions of the piecewise function by connecting the appropriate regions on the coordinate grid. Where the two function values change at \( x = -3 \), you'll see the distinct use of open and closed circles to indicate whether the endpoint is included in a given section of the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc28712d6-8cc5-484b-ae89-313fccbcf9cb%2F8bfd4bbd-fd20-4e86-b692-ab0eb8abd381%2Fuzwavud_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Piecewise Functions**
**Introduction:**
This section explores the concept of piecewise functions through a specific example.
**Function Definition:**
The function \( f(x) \) is defined as a piecewise function:
\[
f(x) =
\begin{cases}
2, & \text{if } x > -3 \\
-2, & \text{if } x \leq -3
\end{cases}
\]
**Graph Explanation:**
The accompanying graph is a coordinate plane with both x and y axes ranging from -10 to 10.
- **For \( x > -3 \):** The function \( f(x) \) evaluates to 2. This is represented by a horizontal line at \( y = 2 \) for all \( x \) greater than -3. This portion of the graph will be an open circle at \( x = -3 \) on the line \( y = 2 \), extending to the right.
- **For \( x \leq -3 \):** The function \( f(x) \) evaluates to -2. This is represented by a horizontal line at \( y = -2 \) for all \( x \) less than or equal to -3. This portion will have a closed circle at \( x = -3 \) on the line \( y = -2 \), extending to the left.
The graph visually distinguishes the two conditions of the piecewise function by connecting the appropriate regions on the coordinate grid. Where the two function values change at \( x = -3 \), you'll see the distinct use of open and closed circles to indicate whether the endpoint is included in a given section of the function.
![Evaluate the function \( f \) at the given value.
\[
f(x) =
\begin{cases}
6x + 1 & \text{if } x < 3 \\
3x & \text{if } 3 \leq x \leq 7 \\
3 - 9x & \text{if } x > 7
\end{cases}
\]
Find \( f(3) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc28712d6-8cc5-484b-ae89-313fccbcf9cb%2F8bfd4bbd-fd20-4e86-b692-ab0eb8abd381%2Faoucqhn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Evaluate the function \( f \) at the given value.
\[
f(x) =
\begin{cases}
6x + 1 & \text{if } x < 3 \\
3x & \text{if } 3 \leq x \leq 7 \\
3 - 9x & \text{if } x > 7
\end{cases}
\]
Find \( f(3) \).
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 4 steps with 4 images
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