Rational Functions Review

Asymptotes

100

How do you find the vertical asymptotes?

Set denominator equal to zero

200

What is the first step to finding the horizontal asymptotes

Look at the degrees of the numerator and denominator

300

What are the asymptotes for 

x/ (x²-1)

Y=0

x= 1, -1

400

What are the asymptotes?

y= 4 + 12/(x-3)

y= 4

X= 3

500

What are the asymptotes?

(9x² - 25)/ (x²-5x-6)

Y = 9

x = -6, +1

Add and subtract

100

(10x - 5)/ (2x+3)  +  (8-4x)/ (2x+3)

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

200

Find the LCM of 

(x²-1) and (x²-3x+2)

(x-1)(x+1)(x-2)

300

3y/(2y²-y) + 2/2y

(5y-1) / (y(2y-1))

400

(3x-5)/ (x²-25) - (2)/(x+5)

x/ (x² - 25)

500

What do you have to have to add fractions

common denominator

variation

100

X and Y are inversely related and y=6 while x=4.

What is k?

K=24

200

Y varies inversely with X.  When x = 4, y=10.  Find k and use it to find y when x = 20.  

y=2

300

What must an inverse function have?

xy = k

400

Write the equation for a function y= 1/x translated up 4 units and left 3 units

y= 1/(x +3) + 4

500

What is the difference between inverse and direct variation

direct both x and y go up or down together

inverse, x goes up when y goes down

Multiply and divide

100

simplify. (x² +2x +1)/ (x³-2x²-3x)

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

x cannot = -1

200

find the product of (x²+6x+8)/(x²+4x+3) and ((x+3)/(x+2)

(x+4)/(x+1) 

For all x except x=-3,-2,-1

300

The area of a rectangle is (x²-4)/2x

What is the length if the width is (x+2)²/2

Width is (x-2)/x(x+2)

400

find the quotient of (x-y)²/(x+y)  and (3x+3y)/(x²-y²)

(x-y)³/3(x+y)

For all real numbers except x cannot = y,-y

500

What values cannot be included in your domain

anything that makes the denominator equal to zero

Solve and domain

100

4/(x +5) =4

x = -4

200

1/x + 2/x = 1/6

x=18

300

x/(x-3) -4 = 3/(x-3)

x=3, extraneous solution, no real solution

400

What is the domain of the following function?

y=1x−7

All real numbers except 7

500

4/(x+2) = x²/(x+2)

x=+2,

-2 is an extraneous solution