1. Section 4.1 – Rational Functions and Asymptotes

2. Graphing and Analyzing Rational Functions
Domain
Vertical Asymptotes (x = )
Horizontal Asymptotes (y = )
Holes (x, y)
Intercepts
Graph

3. Find the equations of the horizontal asymptotes of:

4. Domain:
Vertical Asymptotes:
Horizontal Asymptotes:
Holes:
Intercepts:

5. Domain:
Vertical Asymptotes:
Horizontal Asymptotes:
Holes:
Intercepts:

6. Domain:
Vertical Asymptotes:
Horizontal Asymptotes:
Holes:
Intercepts:

7. Domain:
Vertical Asymptotes:
Horizontal Asymptotes:
Holes:
Intercepts:

8. Extension: The graph contains an hole at x = -3
Note: Cancelled and eliminated
Extension: The graph contains an asymptote at x = 3
Note: not eliminated

9. Domain:
Vertical Asymptotes:
Horizontal Asymptotes:
Holes:
Intercepts:

10. Extension: The graph contains a hole at x = -2
Note: cancelled and eliminated

11. Domain:
Vertical Asymptotes:
Horizontal Asymptotes:
Holes:
Intercepts:

12. Graph the rational function which has the following characteristics
Vert Asymp at x = 1, x = -3
Horz Asymp at y = 1
Intercepts (-2, 0), (3, 0), (0, 2)
Passes through (-5, 2)

13. Graph the rational function which has the following characteristics
Vert Asymp at x = 1, x = -1
Horz Asymp at y = 0
Intercepts (0, 0)
Passes through
(-0.7, 1), (0.7, -1),
(-2, -0.5), (2, 0.5)