Question

The graph below has the same shape as the graph of G(X) = x?, but it isshifted up three units and to the right one unit. Complete its equation. Enterexponents using the caret (1); for example, enter x2 as x^2. Do not include"F(X) =" in your answer.F(x) =

Answer 1

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.