Question

Choose the function that correctly identifies the transformation of f(x) = x 2 shifted two units down and one unit to the left. g(x) = (x - 1)2 - 2 g(x) = (x - 1)2 + 2 g(x) = (x + 1)2 - 2 g(x) = (x + 1)2 + 2

Answer 1

`g(x) = ( { x + 1})^(2) - 2`

Explanation:

The parent function is

`f(x) = {x}^(2)`

A transformation that involves a downward shift h units and a shift to the left k units is of the form:

`f(x + k) - h`

If the function is shifted two units down and and one unit to the left, then

`g(x) = ( { x + 1})^(2) - 2`

Therefore the third choice is correct.