Solving Rational Functions

A rational function can be written in the form

• n(x)/d(x)

• 3x+4

• 4x²+3x+4

• 3^x-7

A vertical asymptote is found by setting the _________= to zero and solving for x 

• Numerator

• Denominator

• Right side 

• Left side

The rational function
 y = 2x²+4x/ 5X²- 3x
has a horizontal asymptote at ____

• y=0

• y=1/5

• y= 2/5

• y=1

Determine the  the x intercept  and vertical asymptotes for for the function. 

• (  -3,0)  VA -5 , -6

• (3,0)   VA 5, -6

• (0,-3) VA  -4, - 7

• ( 0,5)  Va  -3, 6

Label the graph

b

c

d

e

a

y-intercept

Vertical Asymptote

origin

Horizontal Asymptote

x-axis

• y = -2

• y = 0

• y = 1/2

• x = 2

• none

Determine the HA and VA for the graph of the function.

• y = -1
  VA x = -2,2

• y = 2
  VA x = -3, 3

• y = -2
  VA x = -4 ,4

• y = -2
  VA x = -5,5

Find the vertical asymptote.
x²-2x-8
__________
3x-2

• y=2/3

• x=3/2

• x= 2/3

• x=1/3

What are the x-intercept(s) for the function
f(x) = (4x + 12)/(x - 6)

• (-3,0)

• (6,0)

• (0,-2)

• (4,0)

What is the y-intercept for f(x) = (2x - 18)/(2x + 6)

• (-9,0)

• (-3,0)

• (0,-3)

• (0,1)