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.