91Ó°ÊÓ

Find the horizontal asymptote of \(y=\frac{5 x+7}{x+3}\) by dividing the numerator by the denominator. Explain your steps.

Describe the vertical asymptotes and holes for the graph of each rational function. $$ y=\frac{x-1}{(3 x+2)(x+1)} $$

Describe the vertical asymptotes and holes for the graph of each rational function. $$ y=\frac{(x-4)(x+5)}{(x+3)(x-4)} $$

Compare each pair of graphs and find any points of intersection. \(y=\left|\frac{1}{x}\right|\) and \(y=\frac{1}{x^{2}}\)

Write two different complex fractions that simplify to \(\frac{x-2}{x+4}\).

Find the points of discontinuity of \(y=\frac{x(2 x-1)(x+1)}{(x+5)(x+1)}\)

Suppose that \(c\) varies jointly with \(d\) and the square of \(g,\) and \(c=30\) when \(d=15\) and \(g=2 .\) Find \(d\) when \(c=6\) and \(g=8\) .

Solve each equation. Check each solution. $$ \frac{10}{2 y+8}-\frac{7 y+8}{y^{2}-16}=\frac{-8}{2 y-8} $$

Use the tables below for Exercises \(48-50 .\) One student from each school is chosen at random to be on a committee. Find each probability. School A $$ \begin{array}{|c|c|c|c|}\hline \text { Freshman } & {\text { Sophomore }} & {\text { Junior }} & {\text { Senior }} \\ \hline 30 \% & {27 \%} & {25 \%} & {18 \%} \\ \hline\end{array} $$ School B $$ \begin{array}{|c|c|c|c|c|}\hline \text { Freshman } & {\text { Sophomore }} & {\text { Junior }} & {\text { Senior }} \\ \hline 28 \% & {28 \%} & {24 \%} & {20 \%} \\ \hline\end{array} $$ a freshman or sophomore from School \(\mathrm{A}\) and a senior from School \(\mathrm{B}\)

Find the asymptotes of the graph of each equation. $$ y=\frac{3}{x}+4 $$