# Polynomial Functions and Modeling

## Vocabulary

### cubic function

polynomial function of degree 3

### degree of a polynomial

greatest degree of a term in a polynomial

### degree of a term

exponent of the variable of a term in a polynomial in one variable

### end behavior

description of how the values of a function change as the input values approach positive or negative infinity

### even function

function with a graph that is symmetric with respect to the $y$-axis

### global maximum

point where the value of a function is greatest

### global minimum

point where the value of a function is least

the number multiplied by the variable in the first term of a polynomial written in standard form, which places the term with the highest degree first

### local maximum

turning point where a graph changes from increasing to decreasing

### local minimum

turning point where a graph changes from decreasing to increasing

### maximum value

greatest value in the range of a function

### minimum value

least value in the range of a function

### 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.

### odd function

function with a graph that is symmetric with respect to the origin

### polynomial function

function whose rule is a polynomial in one variable, which is a sum or difference of terms of the form $ax^n$, where $a$ is a real number and $n$ is a nonnegative integer

### polynomial in one variable

sum or difference of terms of the form $ax^n$, where $a$ is a real number and $n$ is a nonnegative integer

### power function

function, where $a$ is a nonzero real number and $n$ is a real number, written in the form:
$f(x) = ax^n$

### turning point

point where a graph changes from increasing to decreasing or from decreasing to increasing

### zero of a function

value of $x$ that makes the value of a function zero