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,...
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![### Piecewise Function Graphing
#### Instructions
**Graph the function.**
\[ f(x) = \begin{cases}
3x & \text{for } x \leq -1 \\
-3x & \text{for } x \geq -1
\end{cases} \]
#### Explanation
In this example, you are asked to graph a piecewise function that consists of two linear components.
#### Graph Description
Below the function definition, a coordinate graph is provided. The x-axis ranges from -10 to +10, and the y-axis ranges from -1 to +9. The graph is a standard Cartesian plane with marks at each integer along both axes.
To graph the given piecewise function:
1. **For \( x \leq -1 \) :** Use the equation \( f(x) = 3x \).
- Identify and plot points to the left of \( x = -1 \) using \( y = 3x \).
- For instance, when \( x = -2 \), \( y = 3(-2) = -6 \); and when \( x = -3 \), \( y = 3(-3) = -9 \).
2. **For \( x \geq -1 \) :** Use the equation \( f(x) = -3x \).
- Identify and plot points from \( x = -1 \) towards positive x-values using \( y = -3x \).
- For instance, when \( x = 0 \), \( y = -3(0) = 0 \); and when \( x = 1 \), \( y = -3(1) = -3 \).
Ensure to depict the behavior change at \( x = -1 \) accurately, reflecting the switch in equations from \( 3x \) to \( -3x \).
Using these steps, you should be able to draw the respective parts of the piecewise function on the Cartesian plane provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff89ba37-26bc-4b82-a8cd-348baae55f0e%2F153bf5f4-9dda-4b38-b1c5-e01b5195d079%2Foqe8n8h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Piecewise Function Graphing
#### Instructions
**Graph the function.**
\[ f(x) = \begin{cases}
3x & \text{for } x \leq -1 \\
-3x & \text{for } x \geq -1
\end{cases} \]
#### Explanation
In this example, you are asked to graph a piecewise function that consists of two linear components.
#### Graph Description
Below the function definition, a coordinate graph is provided. The x-axis ranges from -10 to +10, and the y-axis ranges from -1 to +9. The graph is a standard Cartesian plane with marks at each integer along both axes.
To graph the given piecewise function:
1. **For \( x \leq -1 \) :** Use the equation \( f(x) = 3x \).
- Identify and plot points to the left of \( x = -1 \) using \( y = 3x \).
- For instance, when \( x = -2 \), \( y = 3(-2) = -6 \); and when \( x = -3 \), \( y = 3(-3) = -9 \).
2. **For \( x \geq -1 \) :** Use the equation \( f(x) = -3x \).
- Identify and plot points from \( x = -1 \) towards positive x-values using \( y = -3x \).
- For instance, when \( x = 0 \), \( y = -3(0) = 0 \); and when \( x = 1 \), \( y = -3(1) = -3 \).
Ensure to depict the behavior change at \( x = -1 \) accurately, reflecting the switch in equations from \( 3x \) to \( -3x \).
Using these steps, you should be able to draw the respective parts of the piecewise function on the Cartesian plane provided.
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