1. Graphing Rational Functions

2. Graphing Rational Functions
Factor
Determine where discontinuities would occur in the graph
Graph any asymptotes on the graph and pick points on both sides to locate the branches of the function
If factors cancel, then you have a point of discontinuity (hole)
If factors remain in the denominator, you have a vertical asymptote(s)

3. Horizontal Asymptotes
If the degree of the numerator is bigger than the degree of the denominator, then there is NO H.A. (top-heavy)
If the degree of numerator is smaller than the degree of the denominator, then the HA is at y=0 (bottom heavy)
If the degree of numerator is equal to degree of the denominator, then the HA is equal to the leading coefficients (equal weight)

4. Parent Function
𝑓 𝑥 = 1 𝑥
Domain:
Range:
VA:
HA:
Hole:

5. 𝑦= 1 𝑥+2
Domain:
Range:
VA:
HA:
Hole:

6. 𝑦= 𝑥 2 +7𝑥+12 𝑥 2 +9𝑥+20
Domain:
Range:
VA:
HA:
Hole:

7. 𝑦= 3𝑥 2 −13𝑥−10 𝑥−5
Domain:
Range:
VA:
HA:
Hole:

8. 𝑦= 𝑥 2 +2𝑥−3 𝑥 2 +𝑥−2
Domain:
Range:
VA:
HA:
Hole:

9. 𝑦= 𝑥 𝑥 2 −2𝑥−3
Domain:
Range:
VA:
HA:
Hole:

10. 𝑦= 𝑥 2 −9 𝑥−3
Domain:
Range:
VA:
HA:
Hole:

11. 𝑦= 𝑥 2 −9 𝑥 2 −1
Domain:
Range:
VA:
HA:
Hole: