WTMaths logo
Sketch Translations of Functions

Sketch Translations of Functions

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))`.

Example 1

Sketch the graph of `f(x)=x^2`. Then sketch the graph of `f(x+4)`.

Describe the translation.

To translate a function horizontally, apply the add/subtract before evaluating the function.

Answer: The line has been translated `((-4),(0))`

Graph showing translation amend value then function

Example 2

Sketch the graph of `f(x)=x^2`. Then sketch the graph of `f(x)+4`.

Describe the transformation.

To translate a function vertically, apply the add/subtract after evaluating the function.

Answer: The line has been translated `((0),(4))`

Graph showing translation function then amend answer

See also Expressions as Functions and Translation