Section 2.7 Graphing rational functions

Graph f(x)=x/x^2-x-2

set the numerator equal to zero in order to find the x-intercepts

x-intercept = 0

plug in a zero to find the y-intercepts

y-intercept= 0

factor the denominator to find the vertical asymptotes

(be sure to write them as an equation of a line)

(x-2)(x+1)

x=2 x=-1

The horizontal asymptote is y=0 because the numerator degree is less than the denominator degree

Graph the function

(the graph will end up looking like the graph on the right)

Rules for horizontal asymptotes:

1. just use the leading term because the other terms are insignificant

2. If the degrees are the same for the leading term, just divide the numerator by the denominator

3. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote

4. If the numerator degree is less than the denominator degree, the horizontal asymptote is y=0

5. A line can cross the horizontal asymptote in the middle of the graph

6. written as y=

Vertical asymptotes are where the denominator is equal to zero

-you can never cross the vertical asymptote

-written as x=

Be sure to watch out for holes and zeros of multiplicity

F(x)= x (x-3)/ (x^2-x-2)(x-3)

(x-3) is in the numerator and denominator so you cross them out leaving a hole in the graph at x=3

When there is a zero of multiplicity of two, the graph will look exactly the same as the graph on the other side of the asymptote.

F(x)= x/(x-3)

x-intercept= 0

y-intercept=0

vertical asymptote is x=3

horizontal asymptote is y=1