Question

Which of the following functions have y-axis symmetry?
a y=x^2,y= |x|, y= cos(x)
b y=sinx, y = cos x, y = x, y = x^3
c. y=x, y=x^3, y=1/x, y=cos x
d. y=1/x, y=sin x, y=x^2

Answer 1

The plot of a function f(x) is symmetric across the y-axis if it is even, meaning f(-x) = f(x) for all x in the function's domain.

The answer is then A because

(-x)² = (-1)² x² = x²

|-x| = |-1| |x| = |x|

cos(-x) = cos(x)

The answer is not

• B because sin(-x) = -sin(x) and (-x)³ = (-1)³ x³ = -x³

• C because -x ≠ x and again because of x³

• D because 1/(-x) = -1/x and again because of sin(x)