Determine whether the following functions are rational functions. If so, write what $p(x)$ and $q(x)$ are if we write the rational function in the form $p(x)/q(x)$, where $p$ and $q$ are polynomials. If not, enter "NONE" in the provided blank.

a) $f(x) = 4 x^3+7$

? Yes, this is a rational function No, this is not a rational function
$p(x) =$
$q(x) =$

b) $g(x) = \dfrac{4^x+1}{4^x-2}$

? Yes, this is a rational function No, this is not a rational function
$p(x) =$
$q(x) =$

c) $f(x) = \dfrac{x^2}{2-x} - \dfrac{1}{x-2}$

? Yes, this is a rational function No, this is not a rational function
$p(x) =$
$q(x) =$

d) $g(x) = \dfrac{\sqrt{x}+7}{\sqrt{x}}$

? Yes, this is a rational function No, this is not a rational function
$p(x) =$
$q(x) =$

Hint: