Rational Functions

If power of numerator = power of denominator

Horizontal Asymptote is y = C (the ratio of the leading coefficients )

If power of numerator < power of denominator

Horizontal asymptote is at y = 0

If power of numerator > power of denominator

Oblique/Slant Asymptote

When a zero/factor is in the numerator and denominator

Removable Discontinuity

Used to determine the equation of an oblique asymptote

Synthetic/Long Division

Values that are not a part of the domain because they make the denominator zero

Vertical Asymptotes

y = 3

What are the horizontal asymptote?

(-3,0); (1,0)

What are the x-intercepts?

(2,0)

What are the x-intercepts?

(3,0)(-4,0)

What are the x-intercepts?

(4, 0)

What are the x-intercepts?

none

What are the x-intercepts?

x ≠ -2

What is the domain?

x≠0; x≠3

What is the domain?

none

What is the horizontal asymptote?

y = 0

What is the horizontal asymptote??

(0, -1/6)

What is the y-intercept?

(0, 0)

What is the y-intercept?

none

What is the y-intercept?

x=-1; x=3

What is/are the vertical asymptote(s)?

x=3

What is/are the vertical asymptote(s)?

x=3; x=-3

What is/are the vertical asymptote(s)?

Vertical Asymptote at x= 4 and a hole when x = -3

a

Horizontal Asymptote at y=3 and Vertical Asymptote at x = 4

b

Vertical Asymptote at x = 2, hole when x = 1

c

Hole when x = -1, Vertical Asymptote at x = 1

d

Horizontal Asymptote y=0 and a Vertical Asymptote at x = 0

e

Horizontal Asymptote at y=0 and 3 points of discontinuity

f

Vertical Asymptote at x = -3 and x=4

g

Hole at x=0 and 1 other point of discontinuity.

h

No vertical Asymptote

i

Vertical Asymptote at x = 5

j

No horizontal Asymptote and hole at x =4

k

Horizontal Asymptotes at y=1 and y=-1

l

Set the numerator equal to zero

x - intercepts

Substitute x = 0 into the function

y - intercept