Question

Which functions are symmetric about the y-axis?

a) y=x^2
b) y=sin x
c) y =cos x
d) y=e^x

Answer 1

The functions symmetric about the y-axis are y = x^2 and y = cos x because an even function, which satisfies y(x) = y(-x), shows symmetry about the y-axis.

Step-by-step explanation:

To determine which functions are symmetric about the y-axis, we need to know that a function is symmetric about the y-axis if it's an even function. An even function satisfies the condition y(x) = y(-x). Let's analyze the given functions:

• y = x^2 is a quadratic function and is symmetric about the y-axis because (x^2) = (-x)^2.
• y = sin x is not symmetric about the y-axis since sin(x) ≠ sin(-x); instead, it's an odd function because sin(-x) = -sin(x).
• y = cos x is symmetric about the y-axis because cos(x) = cos(-x).
• y = e^x is not symmetric about the y-axis because e^x ≠ e^{-x}; this function is neither even nor odd.

Therefore, the functions symmetric about the y-axis are y = x^2 and y = cos x.