For all your questions, big or small, IDNLearn.com has the answers you need. Our experts provide accurate and detailed responses to help you navigate any topic or issue with confidence.

Select the correct answer.

In which direction must the graph of [tex]$f(x)=|x|$[/tex] be shifted to produce the graph of [tex]$g(x)=|x-3|$[/tex]?

A. down
B. up
C. left
D. right


Sagot :

To determine the direction in which the graph of [tex]\( f(x) = |x| \)[/tex] must be shifted to produce the graph of [tex]\( g(x) = |x-3| \)[/tex], we need to understand how transformations affect the graph of a function.

The function [tex]\( f(x) = |x| \)[/tex] is a standard absolute value function. When a constant is subtracted inside the absolute value, as in [tex]\( g(x) = |x-3| \)[/tex], it causes a horizontal shift. Specifically:
- When you have [tex]\( f(x - c) \)[/tex], the graph shifts [tex]\( c \)[/tex] units to the right if [tex]\( c \)[/tex] is positive.
- When you have [tex]\( f(x + c) \)[/tex], the graph shifts [tex]\( c \)[/tex] units to the left if [tex]\( c \)[/tex] is positive.

In the function [tex]\( g(x) = |x-3| \)[/tex], the [tex]\( -3 \)[/tex] inside the absolute value indicates that the graph will shift 3 units to the right.

Therefore, the graph of [tex]\( f(x) = |x| \)[/tex] must be shifted to the right to produce the graph of [tex]\( g(x) = |x-3| \)[/tex].

The correct answer is:
D. right