How to Test for Symmetry with Respect to the Y-Axis in Math: Step-by-Step Guide and Example

How to test for symmetry for the y-axis

To test for symmetry with respect to the y-axis, you can follow these steps:

Step 1: Write down the equation of the given function

To test for symmetry with respect to the y-axis, you can follow these steps:

Step 1: Write down the equation of the given function. Let’s say the function is f(x).

Step 2: Replace x with -x in the equation of the function.

Step 3: Simplify the equation by performing any required operations.

Step 4: If the resulting equation is equivalent to the original equation, then the function is symmetric with respect to the y-axis. In other words, it exhibits y-axis symmetry.

Let’s illustrate this process with an example:

Example: Determine if the function f(x) = x^3 – 2x + 1 is symmetric with respect to the y-axis.

Step 1: Write down the equation of the given function:
f(x) = x^3 – 2x + 1.

Step 2: Replace x with -x in the equation of the function:
f(-x) = (-x)^3 – 2(-x) + 1

Step 3: Simplify the equation by performing any required operations:
f(-x) = -x^3 + 2x + 1

Step 4: Compare the resulting equation with the original equation:
f(-x) = -x^3 + 2x + 1 and f(x) = x^3 – 2x + 1

Since f(-x) is not equivalent to f(x) (the signs of the terms are different), the function f(x) = x^3 – 2x + 1 is not symmetric with respect to the y-axis.

Remember, for a function to be symmetric with respect to the y-axis, it must satisfy the condition f(-x) = f(x).

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