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Given the parent function f(x) = x², which of the functions listed below would be an equivalent function that has been translated right 3 and up 2? ○g(x) = (x − 3)² – 2

Given the parent function f(x) = x², which of the functions listed below would be an equivalent function that has been translated right 3 and up 2? ○g(x) = (x − 3)² – 2

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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### Problem Statement **Given the parent function** \( f(x) = x^2 \), **which of the functions listed below would be an equivalent function that has been translated right 3 and up 2?** 1. \( g(x) = (x - 3)^2 - 2 \) 2. \( g(x) = (x + 3)^2 + 2 \) 3. \( g(x) = (x - 3)^2 + 2 \) 4. \( g(x) = (x + 3)^2 - 2 \) ### Explanation When translating the parent function \( f(x) = x^2 \): - **Right by 3 units**: We replace \( x \) with \( (x - 3) \) in the function. - **Up by 2 units**: We add 2 to the function. Combining these transformations, we get the function: \[ g(x) = (x - 3)^2 + 2 \] Thus, the correct answer is: - **Option 3: \( g(x) = (x - 3)^2 + 2 \)**
Transcribed Image Text:### Problem Statement **Given the parent function** \( f(x) = x^2 \), **which of the functions listed below would be an equivalent function that has been translated right 3 and up 2?** 1. \( g(x) = (x - 3)^2 - 2 \) 2. \( g(x) = (x + 3)^2 + 2 \) 3. \( g(x) = (x - 3)^2 + 2 \) 4. \( g(x) = (x + 3)^2 - 2 \) ### Explanation When translating the parent function \( f(x) = x^2 \): - **Right by 3 units**: We replace \( x \) with \( (x - 3) \) in the function. - **Up by 2 units**: We add 2 to the function. Combining these transformations, we get the function: \[ g(x) = (x - 3)^2 + 2 \] Thus, the correct answer is: - **Option 3: \( g(x) = (x - 3)^2 + 2 \)**
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