3. Polynomial and Rational Functions

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient.

$f\left(x\right)=4x^3+\frac{1}{2}{x}^{-1}-2x+1$

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient.

$f\left(x\right)=2+x$

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient.

$f\left(x\right)=3x^2+5x+2$

Determine the end behavior of the given polynomial function.

$f\left(x\right)=x^2+4x+x+7x^3$