Below are the graphs f(x) = |x|and its transformation g (x). What is the equation for g(x). -5 -4 -3 -1 3 -4 -4 -5 f(x) = |x| g(x) = ? O g (a) = |æ + 3| + 2 O g (x) = |- æ + 3| + 2 O g(x) = -læl + 2

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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Below are the graphs \( f(x) = |x| \) and its transformation \( g(x) \).

What is the equation for \( g(x) \)?

### Graph Explanation

The first graph displays the absolute value function \( f(x) = |x| \), which is a V-shaped graph symmetric with respect to the y-axis. The vertex of the graph is at the origin (0,0), and it opens upwards.

The second graph shows a transformed version of the absolute value function. It appears to be flipped vertically and shifted horizontally to the left and possibly shifted vertically.

### Multiple Choice Options

- \( g(x) = |x + 3| + 2 \)
- \( g(x) = |-x + 3| + 2 \)
- \( g(x) = -|x| + 2 \)
- \( g(x) = -|x + 3| + 2 \)

The task is to identify the correct equation for \( g(x) \) based on the transformation of the original graph \( f(x) = |x| \).
Transcribed Image Text:Below are the graphs \( f(x) = |x| \) and its transformation \( g(x) \). What is the equation for \( g(x) \)? ### Graph Explanation The first graph displays the absolute value function \( f(x) = |x| \), which is a V-shaped graph symmetric with respect to the y-axis. The vertex of the graph is at the origin (0,0), and it opens upwards. The second graph shows a transformed version of the absolute value function. It appears to be flipped vertically and shifted horizontally to the left and possibly shifted vertically. ### Multiple Choice Options - \( g(x) = |x + 3| + 2 \) - \( g(x) = |-x + 3| + 2 \) - \( g(x) = -|x| + 2 \) - \( g(x) = -|x + 3| + 2 \) The task is to identify the correct equation for \( g(x) \) based on the transformation of the original graph \( f(x) = |x| \).
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