Exploring Symmetry through the Y-Axis: A Guide to Understanding and Identifying Symmetric Functions

Function symmetric through the y-axis

A function is considered symmetric through the y-axis if it remains unchanged when reflected across the y-axis

A function is considered symmetric through the y-axis if it remains unchanged when reflected across the y-axis.

To determine if a function is symmetric through the y-axis, we can compare the corresponding points on each side of the y-axis.

Let’s use an example to demonstrate this concept. Consider the function f(x) = x^2.

To check if this function is symmetric through the y-axis, we evaluate f(x) and f(-x) for different values of x.

Let’s start with x = 2. We have f(2) = 2^2 = 4 and f(-2) = (-2)^2 = 4. Both values are the same, which indicates that the function is symmetric through the y-axis for this particular value of x.

Let’s try another value, say x = 3. We have f(3) = 3^2 = 9 and f(-3) = (-3)^2 = 9. Again, both values are equal, confirming that the function is symmetric through the y-axis for this value of x as well.

We can repeat this process for any other value of x and observe that the function remains the same when reflected across the y-axis. Thus, we can conclude that the function f(x) = x^2 is symmetric through the y-axis.

In general, to determine if a function is symmetric through the y-axis, we compare the values of the function for a given x and its opposite, -x. If the values are equal, the function is symmetric through the y-axis. If not, the function is not symmetric through the y-axis.

More Answers: