Question

Which of the following absolute value equation graphs shifts to the left without graphing it?

(A) f(x) = |x - 2|
(B) f(x) = |x + 3|
(C) f(x) = |x| + 2
(D) f(x) = |x| - 3

Answer 1

Option B: f(x) = |x + 3| shows a translation of 3 units to the left.

Which of the following absolute value equation graphs shifts to the left without graphing it?

For any function f(x), a horizontal translation is defined as:

g(x) = f(x + N)

if N > 0,the translation is to the left.

if N < 0, the translation is to the right.

Here we want to identify the translation to the left, and we can see that it is the second option.

if g(x) = |x|

Then we can write:

f(x) = g(x + 3) = |x + 3|

This is a translation of 3 units to the left.