Topic 4 - Rational Functions

The chart represents an inverse variation. Find the value of p .

Write an equation for the inverse variation represented by the table.

Three students can wash a car in 16 minutes. If the time varies inversely with the number of students washing the car, how many minutes will it take two students to complete that same job?

What is the equation of the horizontal asymptote of the graph of $$y=\frac{1}{x+5}-4$$ ?

Which equation is shown in the graph?

Identify any vertical asymptotes of the graph of $$y=\frac{\left(x+1\right)^2}{x^2-3x-4}.$$

What are the vertical and horizontal asymptotes of the graph of $$f\left(x\right)=\frac{3-2x}{4-3x}\ \ ?$$

A scientist mixes x liters of water into a container that has 10 liters of a mixture that is 12% salt and 88% water. The function $$f\left(x\right)=\frac{1.2}{x+10}$$ represents the percent of salt (in decimals) in the new mixture. How many liters of water must be added to make a 1% salt mixture?

Simplify $$\frac{\left(x+5\right)\left(x^2-25\right)}{\left(x+5\right)^2\left(x-5\right)^2}.$$ What is the domain?

$$Simplify\ \frac{ab^2-a^2b}{ab}\cdot\frac{a^2b^2}{a-b}.$$