Question

If you apply the changes below to the absolute value parent function, f(x) = |Xl,

what is the equation of the new function?
• Shift 5 units to the left.
• Shift 4 units down.

Answer 1

• Shift 5 units to the left >>> f(x) = |x+5|

• Shift 4 units down >>> f(x) = |x| - 4

Explanation:

If we have the parent function:

f(x) = |x|

For horizontal translations:

• |x-a| means horizontally translated a units right
• |x+a| means horizontally translated a units left

For Vertical translation:

• |x| + b means vertically translated b units up
• |x| - b means vertically translated b units down

From the translation rules, we can say:

Shift 5 units left would be:

|x+5|

and

Shift 4 units down would be:

|x| - 4