Rational Functions Test Review

What is the solution of the following?

 $\frac{x-7}{x-1}<0$  

• x<1 or x>7

• x>7

• 1<x<7

• All real numbers

Which statement best describes the graph of

 $\frac{x^2-9}{2x-6}?$  

• The graph has a vertical asymptote at x=3

• The graph has no vertical asymptote

• The graph has a vertical asymptote at x=-3

• The graph has vertical asymptotes at x=3 and x=-3

Which graph represents a function that has the domain (–∞, –4) ⋃ (–4, 3) ⋃ (3, ∞), has a y-intercept at (0, 3), and is increasing on the interval (0, 4)?

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Which of the following equations represents the graph?

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  $f\left(x\right)=\frac{4}{x}$

• $f\left(x\right)=-\frac{4}{x}$

• $f\left(x\right)=\frac{x}{4}$

The equation below shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0?

 $D\ =\ \frac{13}{V}$  

• The density approaches 0.

• The density approaches 1.

• The density approaches 13.

• The density approaches infinity.

What is the solution to the following equation?

 $\frac{x}{x-4}-\frac{4}{x+4}=\frac{32}{x^2-16}$  

• x  =-4, x = 4

• x = 0

• All Real Numbers

• No Solution

Jaisal can mow a lawn in 30 minutes. Sarah takes twice as long to mow the same lawn. If they work together, the situation can be modeled by the following equation, where t is the number of minutes it would take to mow the lawn together in minutes.

 $\frac{1}{30}+\frac{1}{60}=\frac{1}{t}$  

What is the difference of the following?

 $\frac{x}{x^2-4}-\frac{5}{x-2}$  

•  $\frac{-4x+2}{x^2-4}$  

•  $\frac{-2\left(x+5\right)}{\left(x+2\right)\left(x-2\right)}$  

•  $\frac{x-5}{\left(x^2-4\right)-\left(x-2\right)}$  

•  $\frac{x-5}{x^2-4}$