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**
The function \( f(x) \) is defined as follows:
\[
f(x) =
\begin{cases}
x^2 - 1 & \text{for } x \leq 1\\
2x - 2 & \text{for } x > 1
\end{cases}
\]
**Graph Explanation:**
The graph provided is an empty coordinate grid for plotting the piecewise function \( f(x) \). The x-axis ranges from -5 to 5, and the y-axis ranges from -5 to 5.
- For \( x \leq 1 \): The function follows \( f(x) = x^2 - 1 \), a downward-opening quadratic curve.
- For \( x > 1 \): The function follows \( f(x) = 2x - 2 \), a linear function with a slope of 2 and y-intercept of -2.
The task is to graph these two conditions on the provided grid, connecting them appropriately at \( x = 1 \) by evaluating each equation at \( x = 1 \) to ensure continuity or identifying any discontinuities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a54d7d8-382f-4dae-bfd8-b87945b99138%2F78ae9a4d-8e3f-41af-bf6c-952d6a29ef4f%2F8dzyqnp_processed.png&w=3840&q=75)
Transcribed Image Text:**Graph the Function**
The function \( f(x) \) is defined as follows:
\[
f(x) =
\begin{cases}
x^2 - 1 & \text{for } x \leq 1\\
2x - 2 & \text{for } x > 1
\end{cases}
\]
**Graph Explanation:**
The graph provided is an empty coordinate grid for plotting the piecewise function \( f(x) \). The x-axis ranges from -5 to 5, and the y-axis ranges from -5 to 5.
- For \( x \leq 1 \): The function follows \( f(x) = x^2 - 1 \), a downward-opening quadratic curve.
- For \( x > 1 \): The function follows \( f(x) = 2x - 2 \), a linear function with a slope of 2 and y-intercept of -2.
The task is to graph these two conditions on the provided grid, connecting them appropriately at \( x = 1 \) by evaluating each equation at \( x = 1 \) to ensure continuity or identifying any discontinuities.
Expert Solution
Step 1
Consider the function
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education