Question

What transformations change the graph of f(x) to the graph of g(x)?

Answer 1

The graph would be shifted to the LEFT 5 units (because of the 5 in the parenthesis) and shifted DOWN 9 units because of the 9 on the end.

Answer 2

For this case, the parent function is given by:

$f (x) = x ^ 2$

We apply the following transformations:

Horizontal translations:

Suppose that h> 0

To graph y = f (x + h), move the graph of h units to the left.

We have then for h = 5:

$y = (x + 5) ^ 2$

Vertical translations :

Suppose that k> 0

To graph y = f (x) -k, move the graph of k units down.

We then have for k = 9:

$g (x) = (x + 5) ^ 2 - 9$

Answer:

The graph of g (x) is the graph of f (x) 5 units to the left and 9 units to down