-3 if – 2

Algebra and Trigonometry (6th Edition)
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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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suppose that function f is defined as follows

Graph the function F 

 

## Graphing a Piecewise-Defined Function: Problem Type 1

### Function Definition
Suppose that the function \( f \) is defined as follows:
\[
f(x) = \begin{cases} 
-3 & \text{if } -2 \leq x < -1 \\
-2 & \text{if } -1 \leq x < 0 \\
-1 & \text{if } 0 \leq x < 1 \\
0 & \text{if } 1 \leq x < 2 
\end{cases}
\]

### Graph the Function \( f \)
Below is a visual representation of the function \( f(x) \) on a Cartesian plane.

#### Explanation of the Graph
- **Interval \([-2, -1)\)**:
    - The function value is \( -3 \) for \( x \) in the range \([-2, -1)\).
    - This is plotted as a horizontal line at \( y = -3 \) from \( x = -2 \) to \( x = -1 \), with an open circle at \( x = -1 \) indicating that the endpoint is not included.
    
- **Interval \([-1, 0)\)**:
    - The function value is \( -2 \) for \( x \) in the range \([-1, 0)\).
    - This is plotted as a horizontal line at \( y = -2 \) from \( x = -1 \) to \( x = 0 \), also with an open circle at \( x = 0 \).
    
- **Interval \([0, 1)\)**:
    - The function value is \( -1 \) for \( x \) in the range \([0, 1)\).
    - This is plotted as a horizontal line at \( y = -1 \) from \( x = 0 \) to \( x = 1 \), with an open circle at \( x = 1 \).
    
- **Interval \([1, 2)\)**:
    - The function value is \( 0 \) for \( x \) in the range \([1, 2)\).
    - This is plotted as a horizontal line at \( y = 0 \) from \( x = 1 \) to \( x = 2 \), again with an open circle
Transcribed Image Text:## Graphing a Piecewise-Defined Function: Problem Type 1 ### Function Definition Suppose that the function \( f \) is defined as follows: \[ f(x) = \begin{cases} -3 & \text{if } -2 \leq x < -1 \\ -2 & \text{if } -1 \leq x < 0 \\ -1 & \text{if } 0 \leq x < 1 \\ 0 & \text{if } 1 \leq x < 2 \end{cases} \] ### Graph the Function \( f \) Below is a visual representation of the function \( f(x) \) on a Cartesian plane. #### Explanation of the Graph - **Interval \([-2, -1)\)**: - The function value is \( -3 \) for \( x \) in the range \([-2, -1)\). - This is plotted as a horizontal line at \( y = -3 \) from \( x = -2 \) to \( x = -1 \), with an open circle at \( x = -1 \) indicating that the endpoint is not included. - **Interval \([-1, 0)\)**: - The function value is \( -2 \) for \( x \) in the range \([-1, 0)\). - This is plotted as a horizontal line at \( y = -2 \) from \( x = -1 \) to \( x = 0 \), also with an open circle at \( x = 0 \). - **Interval \([0, 1)\)**: - The function value is \( -1 \) for \( x \) in the range \([0, 1)\). - This is plotted as a horizontal line at \( y = -1 \) from \( x = 0 \) to \( x = 1 \), with an open circle at \( x = 1 \). - **Interval \([1, 2)\)**: - The function value is \( 0 \) for \( x \) in the range \([1, 2)\). - This is plotted as a horizontal line at \( y = 0 \) from \( x = 1 \) to \( x = 2 \), again with an open circle
Expert Solution
Step 1

Algebra homework question answer, step 1, image 1

To graph piecewise function make a table for each function as per the given interval

Step 2

First function is f(x)=-3 , interval is from x= -2 to -1

Pick x that are end point of the given interval

While graphing use open circle for < symbol and closed interval for <= symbol

x

y=-3

-2

-3

-1

-3

Step 3

First function is f(x)=-2 , interval is from x= -1 to 0

Pick x that are end point of the given interval

x

y=-2

-1

-2

0

-2

 

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