Understanding Symmetry with Respect to the Y-Axis in Mathematics: Definition, Characteristics, and Testing

symmetric with the y-axis

When a function is said to be symmetric with respect to the y-axis, it means that the function exhibits mirror symmetry, or reflection symmetry, about the y-axis

When a function is said to be symmetric with respect to the y-axis, it means that the function exhibits mirror symmetry, or reflection symmetry, about the y-axis.

In other words, if you were to fold a piece of paper along the y-axis, the graph on one side would perfectly align with the graph on the other side. The two sides are mirror images of each other.

Mathematically, if we have a function f(x), it is symmetric with the y-axis if and only if f(x) = f(-x) for all x in the domain of the function.

To determine if a given function is symmetric with respect to the y-axis, you can follow these steps:

1. Replace x with -x in the original function.
2. Simplify the expression and see if it is equivalent to the original function.

If the two expressions are equal, then the function is symmetric with respect to the y-axis. If not, then it is not symmetric with respect to the y-axis.

For example, let’s consider the function f(x) = x^2.

1. Replace x with -x: f(-x) = (-x)^2 = x^2
2. Simplify the expression: f(-x) = x^2 = f(x)

Since f(-x) = f(x) for all x, we can conclude that the function f(x) = x^2 is symmetric with respect to the y-axis.

Remember, symmetry with respect to the y-axis means that the function appears the same when reflected across the y-axis, resulting in both sides of the graph being identical.

More Answers: