MAT 150 – Class #24

Topics:• Graphing Rational Functions• Asymptotes

• Vertical • Slanted• Horizontals

• Holes

Rational FunctionsThe function f is a rational function if

where P(x) and Q(x) are polynomials and Q(x)

Ex.

AsymptotesVertical Asymptotes (V.A.):

Horizontal Asymptotes (H.A.):

Asymptotes

𝑦=𝑥−2𝑥2

Blue = Vertical AsymptotesRed = Horizontal Asymptotes

Asymptotes𝑦=

𝑥−2𝑥2−𝑥−6

Blue = Vertical AsymptotesRed = Horizontal Asymptotes

Asymptotes

Blue = Vertical AsymptotesGreen = Slant Asymptotes

Vertical AsymptotesFind the vertical asymptotes

How to Determine Horizontal Asymptotes

Consider the function

1. If n < m,

2. If n = m,

3. If n >m ,

Horizontal AsymptotesFind the Horizontal asymptotes

Slant AsymptotesSlant Asymptotes (S.A.):

Holes:

.

Slant Asymptotes and Holes in Graphs

AssignmentPg. 474-477

#1-7 odd

#9-14 all

#15-19 odd

#42, 46, 47