Question

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

Answer 1

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