Question

If the graph of f(x)=|x| is shifted to the left 2 units, which function describes the graph of the new function?

A) g(x) = |x| + 2
B) g(x) = |x + 2]
C) g(x) = |x - 2|
D) g(x) = |x|– 2

Answer 1

The graph of f(x) = |x| shifted to the left by 2 units is described by the function g(x) = |x + 2|, which is a horizontal translation of the original function.

Step-by-step explanation:

If the graph of f(x) = |x| is shifted to the left by 2 units, the new function describing the graph is g(x) = |x + 2|. In algebra, translating a function to the left by a distance d is represented by adding d to the x inside the function notation. Therefore, shifting f(x) = |x| to the left by 2 units gives us g(x) = |x + 2|, which is option B in the multiple-choice question provided.

It is important not to confuse this with options that may add or subtract from the entire function, as these different adjustments would not represent a horizontal shift. Only adding the value inside the absolute value function will perform this horizontal translation.