# 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

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) = x^{2}

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.