1. Sketching Graphs of Rational Functions
PreCalculus
Sketching Graphs
of Rational Functions

2. Sketch the Graph x-int DNE y-int –1/2 Vert asympt x = 2
Horiz asympt y = 0

3. Sketch the Graph x-int 3 y-int –3/2 Vert asympt x = –2
Horiz asympt y = 1

4. Sketch the Graph x-int 3 y-int DNE Vert asympt x = 0, –4
Horiz asympt y = 1

5. Sketch the Graph (x + 3)(x – 3) x-int 3, –3 y-int 9/20
Vert asympt x = 4, –5
(x + 5)(x – 4)
Horiz asympt y = 1

6. Sketch the Graph x-int 0, –3 y-int 0 Vert asympt x = 4, –5, 1
Horiz asympt y = 1

7. Sketch the Graph linear (y=x) or or cubic (y=x3) odd degree
reciprocal (y=1/x)
even degree
reciprocal (y=1/x2) or or

8. Sketch the Graph (more)
x-int 0, 4
y-int 0
Vert asympt x = –1, –3, 1
Horiz asympt y = 1/2