What is an Even or Odd Function?

An even function is a function that is symmetric about the y-axis, meaning f(-x) = f(x) for all x in the domain of the function. Graphically, this means the function's graph is a mirror image when reflected across the y-axis. Examples of even functions include f(x) = x^2 and f(x) = cos(x).

An odd function, on the other hand, is symmetric about the origin, meaning f(-x) = -f(x) for all x in the domain of the function. Graphically, this means the function's graph remains unchanged when rotated 180 degrees about the origin. Examples of odd functions include f(x) = x^3 and f(x) = sin(x).

Functions that don't satisfy either of these conditions are neither even nor odd.

How to Use the Even or Odd Function Calculator

Step 1: Enter the function

In the input field labeled "Enter a function f(x):", type in the mathematical function you want to analyze. Use standard mathematical notation, with "x" as the variable. For example, you might enter "x^2 + 3x + 1" or "sin(x) + cos(x)".

Step 2: Click the "Calculate Parity" button

After entering your function, click the blue "Calculate Parity" button. The calculator will process your input and determine whether the function is even, odd, or neither.

Step 3: Interpret the results

The calculator will display the result below the button. It will state whether the function is even, odd, or neither. Additionally, it will provide a brief explanation of how this conclusion was reached.

Step 4: Analyze different functions

You can repeat the process with different functions to compare their properties. Simply replace the function in the input field and click the "Calculate Parity" button again.

Step 5: Understand the limitations

Keep in mind that this calculator uses numerical methods to approximate the function's behavior. While it's highly accurate for most common functions, it may occasionally produce incorrect results for very complex or unusual functions.