# Rational and Radical Functions

## Vocabulary

### asymptote

line that a graph approaches as one of the variables approaches infinity or negative infinity

### extraneous solution

solution of a step in solving that is not a solution of the original equation

### hole

missing value in a graph such that the graph approaches the same value on both sides

### inverse variation

relationship for variables $x$ and $y$ and constant $k$ that can be written as:
$y = \frac{k}{x}$

### multiplicity

If $x-c$ is a factor of a polynomial function, the multiplicity of the zero $x=c$ is the number of times that the factor appears, or the exponent of the factor.

### radical function

function whose rule can be written using an expression with a variable under a root, such as a square root or cube root:
$f(x)=\sqrt[\scriptsize{n}]{p(x)}$

### rational function

function whose rule can be expressed as a fraction of two polynomials:
$f(x)=\frac{p(x)}{q(x)}$

### reciprocal function

function in the form:
$f(x)=\frac{1}{x}$