Translation of Functions
Mathematics In a Nutshell
Vertical Translation
y = f(x) + a
Moves the graph vertically by a units.
Example 1
y = x^2 + 2 (shifts the graph vertically by 2)
Example 2
y = √x - 3
Example 3
Horizontal Translation
y = f(x+a)
Moves the graph horizontally by -a
Example 1
y = (x+2)^2
Shifts the graph horizontally by -2
Example 2
y = (x-2)
Shifts the graph horizontally by +2
Example 3
Combined Vertical and Horizontal translation
Example 1
y = (x-2)^2 + 3
Example 2
y = 1/x-2 + 1
y= 1/x --> y = 1/x-2 + 1