# 2.5 Horizontal and Vertical Shifts

## Required Videos

Here are the required notes for your convenience.

## Supplemental Videos

Two graphs may look exactly alike in shape, but differ in their positions within the xy-plane.

Adding or subtracting values from a function will shift the graph of the function on the coordinate plane.

If f is a function and c is a positive constant, then the graph of

• is the graph of shifted up c units
• is the graph of shifted down c units
• is the graph of shifted left c units
• is the graph of shifted right c units

### Vertical translations: adding or subtracting after the function (outside the parenthesis) shifts up 3 spaces on the y axis shifts down 2 spaces on the y axis

### Horizontal translations: adding or subtracting with the function (inside the parenthesis) shifts the graph of left 4 spaces on the x axis shifts the graph of right 3 spaces on the x axis

### Vertical & Horizontal translation shifts the graph of up 2 spaces on the y-axis and right 5 on the x-axis.

If , , and Find the coordinates for h(x) = f(x) + 5 and g(x) = f(x – 2)