Even and Odd Functions

A function is an even function if f(x)=f(-x) because any input and its opposite in f(x) or f(-x) would yield the same output which would turn out in a mirror image along the y-axis. For example f(x)=x^2=f(-x)=(-x)^2. For f(x) when the input is 2 the output is 4, when the input is -2 the output is 4. And in the function is f(-x)=x^2 the output ends up being the the same as f(x). Like when you input 2 the output is 4, and if you input -2 the output is 4. So when you graph either function it is symmetrical along the y-axis.


A function is an odd function if f(-x)=-f(x) because now the input and its opposite yield opposite outputs. For example f(x)=x^3. Now f(x) does not equal f(-x) but f(-x)=-f(x). Because of this the graph is no longer symmetrical along the y-axis but it's symmetrical about the origin or symmetrical 2 twice over.