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18. Below are the functions of y= x| and y= x -3. How are the functions related? 10 10 10 -5 -10 O The functions have the same shape They-intercept ofy = x is 0, and the 1-intercept of th second function is -3. OThe functions have the same 1-intercept. The second function is steeper than y = . OThe two functions are the same. The functions have the same shape The -intercept ofy =is 0, and the 1-intercept of the a S

18. Below are the functions of y= x| and y= x -3. How are the functions related? 10 10 10 -5 -10 O The functions have the same shape They-intercept ofy = x is 0, and the 1-intercept of th second function is -3. OThe functions have the same 1-intercept. The second function is steeper than y = . OThe two functions are the same. The functions have the same shape The -intercept ofy =is 0, and the 1-intercept of the a S

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,...
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**Understanding Absolute Value Functions** This image presents a comparison of two functions: \(y = |x|\) and \(y = |x| - 3\). **Graphs Description:** 1. **Graph of \(y = |x|\):** - The graph forms a "V" shape centered at the origin (0, 0). - As \(x\) moves away from zero in either direction, \(y\) increases. - The vertex of the "V" is at the origin. 2. **Graph of \(y = |x| - 3\):** - This graph also forms a "V" shape, similar to \(y = |x|\). - However, the entire graph is shifted downwards by 3 units. - The vertex of this "V" is at (0, -3). **Analysis of the Functions:** - The functions share the same shape, indicating they both are absolute value functions. - For \(y = |x|\), the y-intercept is 0. - For \(y = |x| - 3\), the y-intercept is -3, illustrating a vertical shift downwards. **Choices for Understanding Relationship:** - The graphs have the same shape. The y-intercept of \(y = |x|\) is 0, and the y-intercept of the second function is -3. - The functions have the same x-intercept. The second function is not steeper, but shifted. - The two functions are not identical due to different intercepts.
Transcribed Image Text:**Understanding Absolute Value Functions** This image presents a comparison of two functions: \(y = |x|\) and \(y = |x| - 3\). **Graphs Description:** 1. **Graph of \(y = |x|\):** - The graph forms a "V" shape centered at the origin (0, 0). - As \(x\) moves away from zero in either direction, \(y\) increases. - The vertex of the "V" is at the origin. 2. **Graph of \(y = |x| - 3\):** - This graph also forms a "V" shape, similar to \(y = |x|\). - However, the entire graph is shifted downwards by 3 units. - The vertex of this "V" is at (0, -3). **Analysis of the Functions:** - The functions share the same shape, indicating they both are absolute value functions. - For \(y = |x|\), the y-intercept is 0. - For \(y = |x| - 3\), the y-intercept is -3, illustrating a vertical shift downwards. **Choices for Understanding Relationship:** - The graphs have the same shape. The y-intercept of \(y = |x|\) is 0, and the y-intercept of the second function is -3. - The functions have the same x-intercept. The second function is not steeper, but shifted. - The two functions are not identical due to different intercepts.
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