monomial

roughly, a monomial is a math expression that has one term, has variables and involves only the operations addition, multiplication and exponentiation to positive integer powers

a polynomial is similar to a monomial, without the restriction of having one term

end behavior

rules about the end behavior of a monomial of the form $f(x)=a{x}^n$

if $n$ is even and $a>0$, $\underset{x\to -\infty }{\lim }f(x)=\infty$ and $\underset{x\to \infty }{\lim }f(x)=\infty$
if $n$ is even and $a>0$, $\underset{x\to -\infty }{\lim }f(x)=-\infty$ and $\underset{x\to \infty }{\lim }f(x)=-\infty$
if $n$ is odd and $a>0$, $\underset{x\to -\infty }{\lim }f(x)=-\infty$ and $\underset{x\to \infty }{\lim }f(x)=\infty$
if $n$ is odd and $a>0$, $\underset{x\to -\infty }{\lim }f(x)=\infty$ and $\underset{x\to \infty }{\lim }f(x)=-\infty$