Refresher - Odd Functions

 

 

 

Odd functions

${\displaystyle ƒ\left(x\right)=x3}$ is an example of an odd function.
Again, let ${\displaystyle f\left(x\right)}$ be a real-valued function of a real variable. Then ${\displaystyle f}$ is odd if the following equation holds for all x in the domain of ${\displaystyle f}$:

${\displaystyle -ƒ\left(x\right)=f(-x)}$ or ${\displaystyle ƒ\left(x\right)+f(-x)=0}$

 

 

 

 

 

 

Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about the origin. Examples of odd functions are ${\displaystyle x}$, ${\displaystyle x3}$, ${\displaystyle sin\left(x\right)}$, and ${\displaystyle sinh\left(x\right)}$.

 

 

 

 

 

 

Math 1A/1B: Pre-Calculus by Dr. Sarah Eichorn and Dr. Rachel Lehman is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License Links to an external site..