**Educational Content****Question:**Below is a graph of $ f(x) = |x| $. Sketch $ g(x) = |x| + 4 $ and $ h(x) = |x| - 3 $ on the same axes. How are the graphs of $ g(x) $ and $ h(x) $ different than $ f(x) $? That is, do they move up or down, and by how much?**Graph Explanation:**The graph shown is a V-shaped absolute value function of $ f(x) = |x| $. It appears centered at the origin, with a vertex at the point (0,0). The graph has two linear segments:1. The left segment has a negative slope and decreases as it moves to the left.2. The right segment has a positive slope and increases as it moves to the right.To sketch $ g(x) = |x| + 4 $:- This graph is the same shape as $ f(x) = |x| $ but is shifted 4 units upwards. The vertex will be at (0, 4).To sketch $ h(x) = |x| - 3 $:- This graph is the same shape as $ f(x) = |x| $ but is shifted 3 units downwards. The vertex will be at (0, -3).The transformations are vertical translations:- $ g(x) $ moves the graph of $ f(x) $ up by 4 units.- $ h(x) $ moves the graph of $ f(x) $ down by 3 units.

f(x)=|x| , g(x)=|x| +4 ,h(x)= |x|-3…

2. Below is a graph of f(x) = |x|. Sketch g(x) = |x| + 4 and h(x) = |x|– 3 on the same axes. How are the graphs of g(x) and h(x) different than f(x)? That is, do they move up or down, and by how much?

2. Below is a graph of f(x) = |x|. Sketch g(x) = |x| + 4 and h(x) = |x|– 3 on the same axes. How are the graphs of g(x) and h(x) different than f(x)? That is, do they move up or down, and by how much?

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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