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;
https://brainly.com/question/1461050
