What are odd and even functions?

There are two main types of functions:

  • odd functions: if the input of these functions is negative, the result will be negative; if the input is positive (with the same absolute value of the negative input) the output will be positive:

Examples of odd functions are sin(x), x³, -x, x etc… .

  • even functions: regardless of the sign of the input, the result will always be positive:

Examples are , |x|, 1-, cos(x) etc… .

Graph of the even function f(x)=. As you can see it is symmetrical to the y-axis.
This is the graph of the even function f(x)=2cos(3x), symmetrical to the y-axis. All even functions have this property.
Graph of the odd function f(x)=x³. In the case of odd function, the graph is symmetrical to the x-axis, as you can see here. The upper part is equal to the lowe part.
Graph of the function f(x)=4sin(x)

And this is what you need to know about odd and even functions! If you have any questions, leave a comment and I will be happy to reply!

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