Question

The functions f(x) and g(x) are shown on the graph. f(x) = x² What is g(x)?

a. g(x)=-x^2-4
b. g(x)=(-x)^2-4
c. g(x)=(-x)^2+4
d. g(x)=-x^2+4​

Answer 1

a. g(x) = -x^2 - 4

Explanation:

The function g(x) has been moved/shifted/slid (translated) DOWN 4 units. And the whole graph has been reflected across the x-axis. The way to show these two changes in the equation is by putting a negative in front of the x (causes the reflection) and tack in a " - 4 " at the end of the equation. So only a or b will be possible correct answers because they have that " - 4 " at the end. The negative in front of the x is shown correctly in answer a. In answer b, the negative is inside the parenthesis with the x and getting squared with it in there. That makes it the same as writing only x^2, so that is why answer b is wrong. Try a number if you just want a double check.

g(x) = -x^2 - 4

See the point (1,-5) on the graph of g(x).

g(1) = -1^2 - 4

= -1 - 4

= -5 This checks out. Hope this helps.