Odd function

Definition

An odd function is a function $f(x)$ that satisfies the condition $f(-x) = -f(x)$ for all $x$ in its domain. Graphically, odd functions exhibit symmetry about the origin.

5 Must Know Facts For Your Next Test

1. The graph of an odd function is symmetric about the origin.
2. If $f(x)$ is an odd function, then $-f(x)$ is also an odd function.
3. Polynomials with only odd-degree terms are odd functions.
4. The sum of two odd functions is an odd function.
5. Examples of common odd functions include $f(x) = x^3$ and $f(x) = \sin(x)$.

Review Questions

• What condition must a function satisfy to be considered an odd function?
• How can you determine if a polynomial is an odd function by looking at its terms?
• What type of symmetry do graphs of odd functions exhibit?

Related terms

Even Function:

A function $f(x)$ that satisfies the condition $f(-x) = f(x)$ for all $x$ in its domain, displaying symmetry about the y-axis.

Symmetry:

A property where one half of a figure or graph mirrors the other half.

Transformation: Operations that alter the form of a figure or graph, such as translations, reflections, stretches, and compressions.