91Ó°ÊÓ

Writing Describe the conditions that will produce a rational function with a graph that has no vertical asymptotes.

Graph each pair of functions. Find the approximate point(s) of intersection. \(y=\frac{6}{x-2}, y=6\)

Use the fact that \(\frac{b}{c}=a^{a} \div \frac{c}{d}\) to simplify each rational expression. State any restrictions on the variables. $$ \frac{\frac{9 m+6 n}{m^{2} n^{2}}}{\frac{12 m+8 n}{5 m^{2}}} $$

Basketball A basketball player has made 21 of her last 30 free throws - an average of 70\(\% .\) To model the player's rate of success if she makes \(x\) more consecutive free throws, use the function \(y=\frac{21+x}{30+x}\) a. Graph the function. b. Use the graph to find the number of consecutive free throws the player needs to raise her success rate to 75\(\% .\)

Each pair of values is from a direct variation. Find the missing value. $$ (2.6,4.5),(x, 6.3) $$

Which expression can be simplified to \(\frac{x-1}{x-3} ?\) $$ \begin{array}{ll}{\text { A. } \frac{x^{2}-x-6}{x^{2}-x-2}} & {\text { B. } \frac{x^{2}-2 x+1}{x^{2}+2 x-3}} \\ {\text { C. } \frac{x^{2}-3 x-4}{x^{2}-7 x+12}} & {\text { D. } \frac{x^{2}-4 x+3}{x^{2}-6 x+9}}\end{array} $$

Explain how factoring is used when adding or subtracting rational expressions. Include an example in your explanation.

Solve each equation. Check each solution. $$ c-\frac{c}{3}+\frac{c}{5}=26 $$

Graph each pair of functions. Find the approximate point(s) of intersection. \(y=-\frac{1}{x-3}-6, y=6.2\)

Graph each pair of functions. Find the approximate point(s) of intersection. \(y=\frac{3}{x+1}, y=-4\)