Unit 6 test: Rational Functions

$y$ varies inversely with $x$, and $y = 10$ when $x = 3$. Find $y$ when $x = 5$.

Which equation shows that $y$ varies inversely with $x$?

Find all vertical asymptotes of $f(x) = \dfrac{x + 5}{x^2 - 16}$. Enter the $x$-values.

The graph of $f(x) = \dfrac{6x^2 - x}{3x^2 + 2}$ has horizontal asymptote $y = c$. What is $c$?

The graph of $f(x) = \dfrac{x^2 + 2x - 8}{x - 2}$ has one hole. Give its coordinates as an ordered pair.

Which describes the graph of $y = \dfrac{-3}{x + 1} + 2$?

Simplify $\dfrac{x^2 - 9}{x^2 - 6x + 9}$.

Multiply $\dfrac{2x + 6}{x^2 - 4} \cdot \dfrac{x + 2}{x + 3}$.

Find every value of $x$ excluded from $\dfrac{x - 5}{x + 2} \div \dfrac{x + 1}{x - 3}$.

Simplify $\dfrac{4}{x + 2} - \dfrac{1}{x}$.

Simplify $\dfrac{\dfrac{1}{x} - \dfrac{1}{3}}{x - 3}$.

Solve $\dfrac{5}{x + 1} = \dfrac{3}{x - 1}$.

Find all solutions of $x - \dfrac{12}{x} = 1$.

Solve $\dfrac{x^2}{x + 3} = \dfrac{9}{x + 3}$.

One printer can print a batch of flyers in $6$ hours, and a second printer can print the same batch in $12$ hours. How many hours will the job take if both printers work together?