Question

What is the horizontal and vertical shift for the absolute value function below?

f(x) = |x -5|+ 1

Answer 1

Moving to the right by 5 units

Moving up by 1 unit

Explanation:

The basic absolute value function is f(x) = |x|

The graph vertex is at the origin.

Adding a value inside the absolute value brackets changes the vertex of the graph horizontally.

• Adding a term moves it to the left
• Subtracting a term moves it to the right

Adding a value outside the absolute value brackets changes the vertex vertically.

• Adding a term moves it up
• Subtracting a term moves it down

Here, in the absolute value, we are subtracting by 5, so we move to the right 5

Outside the brackets, we are adding 1, so we move up 1.

-Chetan K