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
Graph the function
![**Graph the Function**
Consider the piecewise function \( f(x) \) given by:
\[
f(x) =
\begin{cases}
x^2 - 4 & \text{for } x \leq 2 \\
2x - 4 & \text{for } x > 2
\end{cases}
\]
**Graph Explanation:**
The graph consists of two parts based on the piecewise definition of the function:
1. **Quadratic Segment \( x^2 - 4 \) for \( x \leq 2 \):**
- This part of the function is a downward-opening parabola.
- The vertex of the parabola is at \( x = 0 \), \( y = -4 \).
- The function is defined for \( x \leq 2 \), so it includes the point at \( x = 2 \) where \( y = 0 \).
2. **Linear Segment \( 2x - 4 \) for \( x > 2 \):**
- This part is a straight line with a slope of 2 and y-intercept at \(-4\).
- The line starts from just after \( x = 2 \) and extends to the right.
**Coordinate System:**
- The x-axis runs from -5 to 5.
- The y-axis runs from -5 to 5.
- Gridlines are marked at each integer value for clarity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a54d7d8-382f-4dae-bfd8-b87945b99138%2Fbb4876cb-4361-45e8-968b-9307606132b7%2Fqds18vg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph the Function**
Consider the piecewise function \( f(x) \) given by:
\[
f(x) =
\begin{cases}
x^2 - 4 & \text{for } x \leq 2 \\
2x - 4 & \text{for } x > 2
\end{cases}
\]
**Graph Explanation:**
The graph consists of two parts based on the piecewise definition of the function:
1. **Quadratic Segment \( x^2 - 4 \) for \( x \leq 2 \):**
- This part of the function is a downward-opening parabola.
- The vertex of the parabola is at \( x = 0 \), \( y = -4 \).
- The function is defined for \( x \leq 2 \), so it includes the point at \( x = 2 \) where \( y = 0 \).
2. **Linear Segment \( 2x - 4 \) for \( x > 2 \):**
- This part is a straight line with a slope of 2 and y-intercept at \(-4\).
- The line starts from just after \( x = 2 \) and extends to the right.
**Coordinate System:**
- The x-axis runs from -5 to 5.
- The y-axis runs from -5 to 5.
- Gridlines are marked at each integer value for clarity.
Expert Solution
Step 1
To graph the given piecewise function, first, we find out some points and then plot the points in the coordinate plane.
Step by step
Solved in 2 steps with 2 images
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