Unit 3 Test Review

Simplify Rational Functions

100

{2(x-2)}/{(x-2)(x+9)}

2/(x+9)

200

(7x)/(2x^2-2x)

7/{2(x-1)}

300

(x-5)/(x^2-25)

1/(x+5)

400

(x^2+9x+18)/(x+6)

x+3

500

(x^2+13x+40)/(x^2-2x-35)

(x+8)/(x-7)

Multiply/Divide Rational Functions

100

1/3 * 5/9

5/27

200

(6x^2)/(x+2)-:(x)/(x+2)

6x

300

(5)/(x+6) *(x+2)/(x+4)

(5x+10)/(x^2+10x+24)

400

{(x+2)}/{(x^2-4)}-:(x+3)/(x-2)

1/(x+3)

500

(x+7)/(x+8) *(x^2+x-56)/(x^2-49)

1

Key Features Rational Functions

100

Find the vertical asymptote(s), horizontal asymptote(s), and hole(s) of the graph: 

f(x)=(x+3)/(x-2)

VA: x=2

HA:y=1

holes: none

200

Describe the vertical asymptote(s), horizontal asymptote(s), and hole(s) of the graph:  f(x)=(x+3)/(x^2-9)=(x+3)/{(x-3)(x+3)  

VA:x=3

HA: y=0

Hole: x=-3

300

Describe the x-intercept and y-intercept of the following graph: (write answer as a point)

y=(x^2+7x+12)/(x^2+3x-4)={(x+4)(x+3)}/{(x-1)(x+4)}

x-intercept:(-3,0)

y-intercept:(0,-3)

400

Find the horizontal asymptote and end behavior of the graph of  y=(x^2+24x-25)/(3x^2+6x+5)

As \ \x \rightarrow \-infty \, f(x) \rightarrow ? 

As \ \x \rightarrow \infty \, f(x) \rightarrow ? 

H.A: y=1/3

 End Behavior: 1/3

500

Describe the vertical asymptote(s), horizontal asymptote(s), and hole(s) for the graph of  f(x)=(3x^2-5x-2)/(x^2-3x+2)= 

VA: X=1

HA: Y=3

Hole: X=2 

Add/Subtract Rational Functions

100

(5)/(12)+(2)/(12)

7/12

200

(9)/(10)-(1)/(5)

7/10

300

(x+1)/(x^2-9)+(x+7)/(x^2-9)

(2x+8)/(x^2-9)

400

(3)/{(x-4)(x+4)}+(x+3)/(x-4)

(x^2+7x+15)/({(x-4)(x+4)}

500

(3)/(x+4)-(1)/(x+6)

(2x+7)/{(x+6)(x+4)}

Math Facts

100

25+45

70

200

How do I find the y-intercept of a simplified rational expression?

Plug in 0 for x

300

What are the factors of 

x²-1

(x+1)(x-1)

400

When dividing a rational function what do we do?

Keep first fraction change sign and flip second fraction

500

How do we find the horizontal asymptote?

look at the degrees