Translation of a function
Initial explanation
We can translate a function vertically or horizontally:
Vertical translation
We have that the graph of G(x) = x² is the red one and the new F(x) is the blue one:
If we want to translate the function vertically we add the number of unities outside the equation:
- if the number is positive it will be translated upwards.
- if the number is negative it will be translated downwards.
We want to translate G(x) 3 unities up, this means that we must add 3 to the equation:
G(x) + 3 = x² + 3
Horizontal translation
If we want to translate the function horizontally we add the number of unities to the x:
- if the number is positive it will be translated to the left.
- if the number is negative it will be translated to the right.
