Write the equation for the graphed function. Absolute value graph shifted left 3 units.

A. f (x) = |x| - 3

B. f (x) = |x + 3|

C. f (x) = |x| + 3

D. f (x) = |x - 3|

D

Step-by-step explanation:

When functions are transformed there are a few simple rules:

• Adding/subtracting inside the parenthesis to the input shifts the function left (+) and right (-).

• Adding/subtracting outside the parenthesis to the output shifts the function up (+) and down (-).

• Multiplying the function by a number less than 1 compresses it towards the x-axis.

• Multiplying the function by a number greater than 1 stretches it away from the x-axis.

The parent function is f (f) = |x|. Since it needs to be shifted to the left, use the first rule above which is to subtract from the input inside the absolute value.

f (x) = |x-3|