Question

use transformations of the absolute value function, f(x)=|x|, to graph the function g(x)=|x−3|. what transformations are needed in order to obtain the graph of g(x) from the graph of f(x)? select all that apply. a. horizontal shift 3 units to the right b. horizontal shrink by a factor of \\(\frac{1}{3}\\) c. horizontal shift 3 units to the left d. vertical stretch by a factor of 3 e. reflection about the x - axis f. vertical shift 3 units down

Explanation:

Step1: Recall Function Transformation Rules

For a function \( f(x) \), the transformation \( f(x - h) \) represents a horizontal shift. If \( h>0 \), it is a shift to the right by \( h \) units; if \( h<0 \), it is a shift to the left by \( |h| \) units.

Step2: Analyze \( g(x) = |x - 3| \) vs \( f(x)=|x| \)

Here, \( g(x)=f(x - 3) \) where \( f(x)=|x| \) and \( h = 3>0 \). So, this is a horizontal shift of \( f(x) \) 3 units to the right. Options B (horizontal shrink), C (left shift), D (vertical stretch), E (reflection), F (vertical shift) do not apply as there is no shrinking, reflection, vertical stretch, or vertical shift, and the shift is to the right, not left.

Answer:

A. Horizontal shift 3 units to the right