Quiz about Topic 4 - Rational Functions

Question 1

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

Accepted Answer

$$y=\frac{-12}{x}$$

Answer

$$y=\frac{x}{-12}$$

Answer

$$y=\frac{-x}{12}$$

Answer

$$y=\frac{12}{x}$$

Question 2

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?

Accepted Answer

24

Answer

20

Answer

22

Answer

26

Question 3

Which equation is shown in the graph?

Accepted Answer

$$p\left(x\right)=2-\frac{1}{2x+4}$$

Answer

$$p\left(x\right)=2-\frac{1}{2x-4}$$

Answer

$$p\left(x\right)=2+\frac{1}{2x+4}$$

Answer

$$2+\frac{1}{2x-4}$$

Question 4

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

Accepted Answer

$$x=\frac{4}{3}\ and\ y=\frac{2}{3}$$

Answer

$$x=\frac{2}{3}\ and\ y=\frac{4}{3}$$

Answer

$$x=\frac{3}{4}\ and\ y=\frac{2}{3}$$

Answer

$$x=\frac{3}{2}\ and\ y=\frac{4}{3}$$

Question 5

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?

Accepted Answer

$$\frac{1}{x-5};\ all\ real\ numbers\ except\ -5\ and\ 5$$

Answer

$$\frac{x+5}{x-5};\ all\ real\ numbers\ except\ -5\ and\ 5$$

Answer

$$\frac{1}{x+5};\ all\ real\ numbers\ except\ 0$$

Answer

$$\frac{x-5}{x+5};\ all\ real\ numbers\ except\ -5$$

Question 6

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

Accepted Answer

$$-a^2b^2;\ a e0;\ b e0$$

Answer

$$\frac{a^2b^2}{a-b};\ all\ real\ numbers\ except\ 0$$

Answer

$$\frac{b-a}{ab};\ a e0\ or\ b;\ b e0\ or\ a$$

Answer

$$ab^2-a^2b;\ a e0\ or\ b;\ b e0\ or\ a$$

Question 7

$$What\ is\ the\ quotient\ of\ \frac{9-x^2}{3x}and\ \frac{x^2+6x+9}{3x}?$$

Accepted Answer

$$\frac{3-x}{x+3}$$

Answer

$$\frac{x-3}{3-x}$$

Answer

$$\frac{x-3}{x+3}$$

Answer

$$\frac{x+3}{x-3}$$

Question 8

The area of a rectangle is $$\frac{x^2-4}{2x}in.^2$$ and its length is $$\frac{\left(x+2\right)^2}{2}in.\ $$ What is the width in inches?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 9

$$Add\ \frac{5}{2x+1}+\frac{8}{4x+2},\ with\ x e-\frac{1}{2}.$$

Accepted Answer

$$\frac{9}{2x+1}$$

Answer

$$\frac{13}{4x+2}$$

Answer

$$\frac{5x+8}{4x+2}$$

Answer

$$\frac{18}{2x+1}$$

Question 10

$$Subtract\ \frac{3}{x-1}-\frac{4}{x+3}.$$

Accepted Answer

$$\frac{-x+13}{\left(x-1 ight)\left(x+3 ight)};\ x e-3\ or\ 1$$

Answer

$$\frac{-x+5}{\left(x-1 ight)\left(x+3 ight)};\ x e-3\ or\ 1$$

Answer

$$\frac{7x+5}{\left(x-1 ight)\left(x+3 ight)};\ x e-3\ or\ 1$$

Answer

$$\frac{7x+13}{\left(x-1 ight)\left(x+3 ight)};\ x e-3\ or\ 1$$

Question 11

$$Simplify\ \frac{\frac{1}{x}-\frac{1}{x+2}}{2}.$$

Accepted Answer

$$\frac{1}{x\left(x+2 ight)};\ x e-2\ or\ 0$$

Answer

$$\frac{1}{x+2};\ x e-2$$

Answer

$$\frac{1}{x};\ x e0$$

Answer

$$\frac{1}{x\left(x-2 ight)};\ x e2\ or\ 2$$

Question 12

The equation $$r\ =\ \frac{1}{\frac{1}{r_1}+\frac{1}{r_2}}\ $$ represents the total resistance, r, when two resistors whose resistances are r₁and r₂ are connected in parallel. Find the total resistance when r₁ is x and r₂ is x + 1 .

Accepted Answer

$$\frac{x\left(x+1 ight)}{2x+1};\ x e-1,\ -\frac{1}{2},\ or\ 0$$

Answer

$$\frac{1}{2x+1};\ x e-1,\ -\frac{1}{2},\ or\ 0$$

Answer

$$2x+1;\ x e-1\ or\ 0$$

Answer

$$\frac{2x+1}{x\left(x+1 ight)};\ x e-1\ or\ 0$$

Question 13

In still water, the speed of a boat is 10 mi/h. Camilla drives the boat 5 miles upstream and 5 miles back to her starting point in an hour and 20 minutes. What is the speed of the stream?

Accepted Answer

5 mi/h

Answer

2 mi/h

Answer

3 mi/h

Answer

4 mi/h

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