Rational Functions Review

Graphing

100

What are the horizontal asymptotes and vertical asymptotes of 4/(x-3)  +5

VA: x=3

HA: y=5

200

What are the asymptotes of -5/(x+7) -3

HA: y=-3

VA: x=-7

300

What are the reference points of -1/(x+2)-3?

(-3, -2) and (-1, -4)

400

What are the reference points of (3x+1)/(x+1)?

(0,1) and (-2,5)

500

What are the asymptotes of (-2x+1)/(x+1)?

HA: y=-2

VA: x=-1

Operations

100

(x+3)/(x-6)   +   (4x-5)/(x-6)

(5x-2)/(x-6) ex sol: 6

200

(x)/(x-9) * (3x-27)/(x+1)

3x/(x+1)  ex sol: 9, -1

300

2/x - 3/(x-5)

(-x-10)/x(x-5)   ex sol: 0,5

400

5/(x+2) + 6/(x-3)

(11x-3)/(x+2)(x-3)   ex sol: -2, 3

500

(x²-x-12)/(3x-9) divided by (x-4)/12

4   ex sol: 3, 4.  so no solution

Equations

100

5/(x+1) = 2/(x+4)

x=-6

200

4/(x²-4) = 1/(x-2)

no solution

300

3/(x+2) + 3/(2x+4)=x/(2x+4)

x=9

400

2-10/x=3

x=10

500

(x²-7x+10)/x +1/x= x+4

x=1

Inequalities

100

The first step in solving a rational inequality is to ...?

move all terms to the same side of the equation

200

10 < (6x+42)/(x+5)

(-5, -2]

300

24x/2x² > -4

(-infinity, -3) U (0, infinity)

400

(x+1)/(x-3) < (x+2)/(3x-9)

(-0.5, 3)

500

(x-4)/(x²-4) < 2/(x+2)

(-2, 0) U (2, infinity)

Word Problems

100

It takes Ms. Harrison 2 hours to grade tests. It takes Ms. Jarotski 1.5 hours to grade tests. How long would it take it they worked together?

6/7 hours, or 0.86 hours.

200

It takes a fireman 30 minutes to put out a fire. His friend can put out the same fire in 50 minutes. How long would it take if they worked together?

18.75 minutes.

300

It takes Jessica 5 hours to mow her grass. Her sister can finish in 2 hours. How long would it if they worked together?

1.4 hours

400

Betty can paint her house twice as fast as her friend. Together, it takes them 8 hours. How long would it take Betty to work by herself?

12 hours

500

Ray is three times faster than his dad at raking leaves. Together, they can finish this is 4 hours. How long would it take his dad to do the project by himself?

16 hours