Sketch Translations of Functions

# Sketch Translations of Functions

GCSE(H)

Graphs can be translated horizontally and vertically.

To translate the graph horizontally, add or subtract a value before the function is applied. The movement is in the opposite direction to the value of the addition or subtraction. If y = f(x) then f(x + a) will cause the graph to be translated by ((-a),(0)).

To translate a graph vertically, add or subtract a value after the function is applied. That is, if y=f(x) then y=f(x)+a will result in a translation of ((0),(a)).

## Examples

1. Sketch the graph of f(x)=x^2. Then sketch the graph of y=(x+3)^2 - 2.

The function f(x)=x^2 passes through (0, 0).
The addition of +3 before the function is evaluated causes a translation of ((-3),(0)). The subtraction of -2 after the function is evaluated results in translation of ((0),(-2)). Adding the translations gives ((-3),(-2)).
2. The function y=f(x) requires to be translated by ((0), (-2)). What is the new function?
Answer: y=f(x)-2