Choose the correct term to complete each sentence. To find the limits of rational functions at infinity, divide the numerator and denominator by the _

True or False. The graph of a rational function may intersect a horizontal asymptote.

(a) How do you find vertical asymptotes of rational functions? (b) Let s be the rational function ${\displaystyle s\left(x\right)=\frac{a_n{x}^n+a_{n-1}{x}^{n-1}+\cdots +a_{1}x+a_0}{b_m{x}^m+b_{m-1}{x}^{m-1}+\cdots +b_{1}x+b_0}\mathrm{\$}\mathrm{\$}}$
How do you find the horizontal asymptote of s? (c) Find the vertical and horizontal asymptotes of ${\displaystyle f\left(x\right)=\frac{5x^2+3}{x^2-4}}$

I want a function that passes through the (x,y) points (3,0),(4,-1),(6,3) and (7,2). Using Lagrange interpolation I get
${\displaystyle -\frac{x^3-15x^2+70x-102}{2}}$ but using this interpolation method for rational functions I get the much simpler ${\displaystyle \frac{(x-3)}{(x-5)}}$. This is a case where the rational function interpolation is a lot simpler than polynomial interpolation.
Is there a method to get ${\displaystyle \frac{(x-3)}{(x-5)}}$ given the points above, a sort of interpolation method that uses rational functions?

Use substitution to convert the integrals to integrals of rational functions. Then use partial fractions to evaluate the integrals.
${\displaystyle \int \frac{1}{2+e^{-x}}dx}$

Find the parent function (f) of
${\displaystyle h\left(x\right)=|x+3|-5}$

True or False. The domain of every rational function is the set of all real numbers.

This ideal gas law states that the volume of an enclosed gas at a fixed temperature varies inversely as the pressure.
Which power functions are also rational functions?