If a function f is an even function, then what type of symmetry does the graph of f have?
The function f has symmetry with respect to the x-axis
The function f has symmetry with respect to the origin 
The function f has symmetry with respect to the y-axis

Solution:

We know that

A function is even if f(x) = f(-x) for all the values of x in its domain.

It means that the function is the same for positive and negative x axis or is graphically symmetric about the y-axis.

Consider f(x) = x²

f(-x) = (-x)² = x²

Thus we observe f(x) = f(-x)

Therefore, the function f has symmetry with respect to the y-axis.

If a function f is an even function, then what type of symmetry does the graph of f have?

Summary:

If a function f is an even function, then the function f has symmetry with respect to the y-axis.