Question

The graph of the function y = x2 + 2 is shown. Which equation will shift the graph of the function down 4 units?

A) y = x2 + 6
B) y = x2 - 2
C) y = (x + 4)2 + 2
D) y = (x - 4)2 + 2

Answer 1

Answer: OPTION B.

Explanation:

Below are shown some transformations for a function f(x):

1) If
`f(x)+k`, the function is shifted up "k" units.

2) If
`f(x)-k`, the function is shifted down "k" units.

In this case you have the following function, which you can call f(x):

`y =f(x)= x^2 + 2`

Based on the transformations explained before, if this function is shifted down 4 units, you know that function obtained g(x) is:

`g(x)= x^2 + 2-4\\\\g(x)= x^2 -2`

Therefore, the equation that will shift the graph of the function down 4 units, is:

`y= x^2 -2`