Question

Which of the following functions will have the same x-intercept(s) as its reflection about the origin?(1 point)

y=−1/2x+6


y=(x−4)2


y=x2


y=2x−5

Answer 1

y = x^2

Reason: reflection about the origin gives g(x) = -f(-x), and g(x)=0 iff f(-x)=0. So the x-intercepts must be unchanged under x -> -x. x^2 has the single x-intercept x=0, which is symmetric; the others have intercepts 12, 4, and 2.5, respectively, which become -12, -4, and -2.5 after reflection.