Homework Help is Here – Start Your Trial Now!
Math
Algebra
Below is the graph of y=x. Translate it to make it the graph of y = |x − 2| + 1. KIEVE + X Ś ?

Below is the graph of y=x. Translate it to make it the graph of y = |x − 2| + 1. KIEVE + X Ś ?

Algebra and Trigonometry (6th Edition)
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,...
See similar textbooks
icon
Related questions
Question
### Translating the Graph of Absolute Value Functions **Instruction:** Below is the graph of \( y = |x| \). Translate it to make it the graph of \( y = |x - 2| + 1 \). --- **Graph Explanation:** The provided graph represents the function \( y = |x| \), which is a V-shaped graph. - The vertex of the graph is at the origin (0,0). - The graph is symmetric about the y-axis. - The arms of the V extend linearly upward with slopes of 1 on the right and -1 on the left. **Steps to Translate the Graph:** 1. **Horizontal Shift:** - The graph \( y = |x - 2| \) represents a horizontal shift of the graph \( y = |x| \) 2 units to the right. - This moves the vertex from (0,0) to (2,0). 2. **Vertical Shift:** - Adding 1 to the entire function, i.e., \( y = |x - 2| + 1 \), shifts the moved graph vertically upwards by 1 unit. - This further moves the vertex from (2,0) to (2,1). **Resulting Graph:** - The final graph of \( y = |x - 2| + 1 \) has its vertex at (2,1). - The shape of the graph remains a V, symmetric about the vertical line \( x = 2 \). - As before, the arms of the V extend linearly, with the right side having a slope of 1 and the left side having a slope of -1 relative to the new vertex. By following these transformations, the graph of \( y = |x| \) has been effectively shifted rightward and upward to yield the graph of \( y = |x - 2| + 1 \).
Transcribed Image Text:### Translating the Graph of Absolute Value Functions **Instruction:** Below is the graph of \( y = |x| \). Translate it to make it the graph of \( y = |x - 2| + 1 \). --- **Graph Explanation:** The provided graph represents the function \( y = |x| \), which is a V-shaped graph. - The vertex of the graph is at the origin (0,0). - The graph is symmetric about the y-axis. - The arms of the V extend linearly upward with slopes of 1 on the right and -1 on the left. **Steps to Translate the Graph:** 1. **Horizontal Shift:** - The graph \( y = |x - 2| \) represents a horizontal shift of the graph \( y = |x| \) 2 units to the right. - This moves the vertex from (0,0) to (2,0). 2. **Vertical Shift:** - Adding 1 to the entire function, i.e., \( y = |x - 2| + 1 \), shifts the moved graph vertically upwards by 1 unit. - This further moves the vertex from (2,0) to (2,1). **Resulting Graph:** - The final graph of \( y = |x - 2| + 1 \) has its vertex at (2,1). - The shape of the graph remains a V, symmetric about the vertical line \( x = 2 \). - As before, the arms of the V extend linearly, with the right side having a slope of 1 and the left side having a slope of -1 relative to the new vertex. By following these transformations, the graph of \( y = |x| \) has been effectively shifted rightward and upward to yield the graph of \( y = |x - 2| + 1 \).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS