How to use the graph to determine if the function is even, odd, or neither?

Functions are a very integral part of almost every field in mathematics. There can be different types of functions like quadratic, cubic, biquadratic, etc. Functions can be represented in graphs. They can be even, odd, or neither. Let's see how we can determine if a particular function is even, odd, or neither.

Answer: To determine whether if a particular function is even, odd, or neither, we check its symmetry about the y-axis or the origin of the graph.

An odd function is always symmetric about the origin, while even is symmetric about the x-axis.

Explanation:

In case of odd functions:

f(-x) = -f(x)

In case of even functions:

f(-x) = f(x)

If f(x) is neither equal to f(-x) nor equal to f(-x), then we can simply say that it is neither odd nor even.

For a particular function to be even, the graph of that function must be symmetric about the y-axis.

For example, if you check the graph of y = x², it is an upward parabola with its vertex at the origin. It is clearly symmetric to the y axis, and hence it is even. You can verify using the formula f(-x) = f(x) as well.

For a particular function to be odd, the graph of that function must be symmetric about the origin.

For example, if you check the graph of y = x³, it is a cubic curve with its vertex at the origin. It is clearly symmetric to the origin, and hence it is odd. You can verify using the formula f(-x) = -f(x) as well.

Hence, to determine whether if a particular function is even, odd, or neither, we check its symmetry about the y-axis or the origin of the graph.