1. Asymptotes Horizontal Asymptotes Vertical Asymptotes
A rational function may have a vertical asymptote or a horizontal asymptote or both.
Horizontal Asymptotes
When the degree of the numerator is less than the degree of the denominator, the line y = 0 is the horizontal asymptote.
Vertical Asymptotes
Find the values of x that make the denominator equal to zero, but do not make the numerator equal to zero.
y = 0 is the horizontal asymptote
When the degree of the numerator is equal to the degree of the denominator, the equation of the horizontal asymptote is
y = the ratio of the coefficients of the
highest degree terms.
The equations of the vertical asymptotes are these values of x.
When the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.
When x = 1, the numerator does not equal zero. Therefore, there is vertical asymptote at x = 1.
No horizontal asymptote

2. Finding Asymptotes
Find the vertical and horizontal asymptotes if there are any.
Vertical Asymptote
Vertical Asymptote
Vertical Asymptote
Reject
Horizontal Asymptote
Horizontal Asymptote
Horizontal Asymptote
Degree of the numerator equals degree of the denominator.
Degree of the numerator is less than degree of the denominator.
Degree of the numerator is more than degree of the denominator.
No Horizontal Asymptote

3. More Finding Asymptotes
Find the vertical and horizontal asymptotes if there are any.
Vertical Asymptote
Vertical Asymptote
Vertical Asymptote
Horizontal Asymptote
Degree of the numerator equals degree of the denominator.
Horizontal Asymptote
Horizontal Asymptote
Degree of the numerator equals degree of the denominator.
Degree of the numerator is more than degree of the denominator.
No Horizontal Asymptote

4. Homework Page 88: 13 - 23 Find Vertical Asymptotes
And Horizontal Asymptotes

5. Infinite Limits
A graph in which f(x) increases or decreases without bound as x approaches c is called an Infinite Limit. x
1.5
1.9
1.99
1.999 2
2.001
2.01
2.1
2.5
f(x) -6
-30
-300
-3000
3000
300 30 6

6. Infinite Limits From a Graph

7. More Infinite Limits
That was easy

8. Determining Limits
Find the limit of each.
Asi De Facil

9. Homework
Page 88: 38 – 48
Even Numbers