Which functions are symmetric about the y-axis? Check all of the boxes that apply.

The functions that are symmetric about the y-axis are;

1) The function in the first option; f(θ) = cos(θ)

2) The function in the third option; f(x) = x²

Reason for the above selection;

Definition;

A function is symmetric about the y-axis is also known to be an even function such that the same value of the function is arrived at when x is replaced with -x

Analysis of the graphs;

First Function Graph; The graph represents the graph of cos (θ)

∴ The function is f(θ) = cos(θ)

The value of the function when x = π, f(π) = -1

Similarly, the value of the when x = -π, f(-π) = -1

f(π) = f(-π)

∴ f(x) = f(-x)

Therefore; the first function is an even function

Second Function Graph; The function of the graph is x = y²

∴ y = √(x)

The value of the function when x = 4, y = f(4) = 2

However, the when x = -4, f(-4) does not exist

f(4) ≠ f(-4)

∴ f(x) ≠ f(-x)

Therefore; the second function is not an even function (the function, x = y², is however symmetric about the x-axis)

Third Function Graph; The function the graph represents is y = x²

The value of the function when x = 2, f(2) = 4

Similarly, the value of the when x = -2, f(-2) = 4

f(2) = f(-2)

∴ f(x) = f(-x)

Therefore; the third function is an even function

From the above, the functions which are symmetric about the y-axis, (even functions) are;

The first and the third functions

Learn more about symmetric functions here;

link

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step-by-step explanation:

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