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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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47786e8c-2a51-4f4e-a0fc-479b515f394a%2Ff91b0b58-928a-4470-ac59-79cb579f9099%2Fnuwy5c2.jpeg&w=3840&q=75)
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
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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