### Piecewise Function Graphing#### Instructions**Graph the function.**\[ f(x) = \begin{cases} 3x & \text{for } x \leq -1 \\-3x & \text{for } x \geq -1 \end{cases} \]#### ExplanationIn this example, you are asked to graph a piecewise function that consists of two linear components. #### Graph DescriptionBelow 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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Answered: Graph the function. 3x for x<-1 f(x) =…

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Graph the function. 3x for x<-1 f(x) = - 3x for x>-1

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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Question

### 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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