Power function

Definition

A power function is of the form $f(x) = ax^n$ where $a$ and $n$ are constants. The constant $a$ is known as the coefficient, and $n$ is called the exponent.

5 Must Know Facts For Your Next Test

1. The degree of a power function is determined by the exponent $n$.
2. If $n$ is a positive integer, the graph of the power function either increases or decreases without bound.
3. Power functions with even exponents are symmetric about the y-axis, while those with odd exponents are symmetric about the origin.
4. The end behavior of a power function depends on both the sign and magnitude of the coefficient $a$.
5. When graphing power functions, points such as $(1, a)$ and $(0,0)$ (if defined) can serve as helpful reference points.

Review Questions

• What is the general form of a power function?
• How does the exponent $n$ affect the symmetry of a power function's graph?
• Describe how to determine the end behavior of a power function.

Related terms

Polynomial Function: A mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Rational Function: A ratio of two polynomial functions.

End Behavior: The behavior of a graph as its input approaches positive infinity or negative infinity.