Question

If the function y=x2−4
is reflected about the origin, which of the following is true regarding the number of x-intercepts of the reflected function?

Hint: Sketch a graph of the function y=x2−4
, then sketch a graph of the function reflected about the origin.

Option #1: 0 x-intercepts

Option #2: 1 x-intercept

Option #3: 2 x-intercepts

(1 point)
Option #

Answer 1

Reflecting the graph about the origin maps (x,y) to (−x,−y), so the reflected function is
g(x) = −f(−x) = −( (−x)^2 − 4 ) = −(x^2 − 4) = −x^2 + 4.
Solve −x^2 + 4 = 0 → x^2 = 4 → x = ±2.

So there are 2 x-intercepts. (Option #3)