1. Rational Expressions
GRAPHING

2. Objectives
Graph a rational function, find its domain, write equations for its asymptotes, and identify any holes (point discontinuity) in its graph.

3. Glossary Terms asymptote horizontal asymptote point discontinuity
rational function
vertical asymptote
y-intercept

4. Rational Function An equation in the form
Where p(x) and q(x) are polynomial functions and q(x)0.

5. When graphing rational functions
State domain
Find Vertical Asymptote(s)
Find Point of Discontinuity in the graph (HOLES)
Find Horizontal Asymptote
Find the y-intercepts & x-intercepts
Sketch

6. Domain: (-∞,-5) U (-5,1) U (1,∞) Vertical Asymptote(s) x=1 & x=-5
State Domain
Find Vertical Asymptote(s)
Find Point of Discontinuity in the graph
Domain: (-∞,-5) U (-5,1) U (1,∞)
Vertical Asymptote(s) x=1 & x=-5
Find Point of Discontinuity in the graph - none

7. H.A.  y = 0 Find Horizontal Asymptote
Compare the degree of the numerator to the degree of the denominator
degree of the numerator < degree of the denominator
H.A.  y = 0

8. Find Horizontal Asymptote
Compare the degree of the numerator to the degree of the denominator
degree of the numerator < degree of the denominator
H.A.  y = 0
degree of the numerator = degree of the denominator
H.A.  y = the ratio of the lead coefficients.
degree of the numerator > degree of the denominator
none

9. Find y-intercept
Substitute zero for x and find the value of the function

10. Sketch the graph Vertical Asymptotes Horizontal Asymptote y-intercept
Plot a few points x y
-10
.05
-5.5
.92
-4.5
-1.1 .5
1.5 10
.02

11. Domain: (-∞,-6) U (-6,-1) U (-1,∞) Vertical Asymptote(s) x=-1 4
State the domain
Find Vertical Asymptote(s)
Find Point of Discontinuity in the graph
Domain: (-∞,-6) U (-6,-1) U (-1,∞)
Vertical Asymptote(s) x=-1
Find Point of Discontinuity at -6

12. H.A.  y = the ratio of the lead coefficients.
Find Horizontal Asymptote
Compare the degree of the numerator to the degree of the denominator
degree of the numerator = degree of the denominator
H.A.  y = the ratio of the lead coefficients.
y = 1

13. Find y-intercept
Substitute zero for x and find the value of the function

14. Sketch the graph Vertical Asymptote Point of Discontinuity
Horizontal Asymptote
y-intercept
Plot a few points x y
-10
1.8 -2 8
-.5
-13 1
-2.5 10 .4

15. Vertical Asymptote(s) NONE Find Point of Discontinuity at -46
State the Domain
Find Vertical Asymptote(s)
Find Point of Discontinuity in the graph
Domain: (-∞,-4) U (-4,∞)
Vertical Asymptote(s) NONE
Find Point of Discontinuity at -4

16. H.A.  there is no horizontal asymptote
Find Horizontal Asymptote
Compare the degree of the numerator to the degree of the denominator
degree of the numerator > degree of the denominator
H.A.  there is no horizontal asymptote

17. Find y-intercept
Substitute zero for x and find the value of the function

18. Sketch the graph Point of Discontinuity y-intercept Plot a few pointsx y -5 -9 -3 -7 4

19. Homework – day 1 Rational Functions Worksheet 1, part A & B
Graphing Rational Function Worksheet #1-3, 5

20. Graphing Rational Expressions Oblique Asymptotes
To find Oblique (Slant) Asymptotes you will need to divide.

21. Homework – day 2
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