Question

Assuming g(x) = x2 + 3, what is the change made to g(x) if the parent function is f(x) = x2?

A. Vertical translation of 3 units up
B. Vertical translation of 3 units down
C. Horizontal translation of 3 units to the right
D. Horizontal translation of 3 units to the left

How many units and in what direction will the function g(x) = (x + 5)2 - 9 translate if the parent function is f(x) = x2?

A. 9 units to the left 5 units down
B. 9 units to the left 5 units up
C. 5 units to the left and 9 units down
D. 5 units to the left and 9 units up

Answer 1

b

Answer 2

b

Answer 3

\[f(x) + a\]is a vertical translation of \(f(x)\) by \(a\) units. You should be able to work out the direction by comparing the result of \(f(0)\) and \(f(0)+a\).

\[f(x-a)\]is a horizontal translation of \(f(x)\) by \(a\) units. Again, you should be able to work out the direction by trying a few points.

You can do these things in combination. \[f(x-a)+b\]is a horizontal translation of \(f(x)\) by \(a\) units and a vertical translation by \(b\) units.

Dangers of just taking answers from someone like @FATBOI2K12 who doesn't show you how to find the correct answer: the answer may be wrong! I strongly suggest you carefully plot the functions and find the answers for yourself.