The function f (x) = x2 - 9 is shifted 2 units up and 3 units to the left. Select the new function. A) g (x) = 2x2 - 6 B) g (x) = (x - 3) 2 + 7 C) g (x) = 3x2 - 7 D) g (x) = (x + 3) 2 - 7

We have the following function:

f (x) = x ^ 2 - 9

Applying the transformations we have:

Vertical translations

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

h (x) = x ^ 2 - 9 + 2

h (x) = x ^ 2 - 7

Horizontal translations

Suppose that h> 0

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

g (x) = (x + 3) ^ 2 - 7

Answer:

D) g (x) = (x + 3) ^ 2 - 7