Question

The function f(x)=3 (x+6)^2+8 is shifted 4 units up and 3 units right to form another function g(x). What is g(x)?

Answer 1

`g(x) = 3\cdot (x+3)^(2)+12`

Explanation:

There are two operations involved:

Vertical translation:

`f'(x) = f(x) \pm c,\,c\in \mathbb{R}` (1)

Note: Positive sign represent a translation upwards.

Horizontal translation:

`f'(x) = f(x\pm c), x\in \mathbb{R}` (2)

Note: Positive sign represent a translation leftwards.

Then, the new function must be:

`g(x) = f(x-3)+4`

`g(x) = 3\cdot (x+3)^(2)+12`