1. A Summary of Curve Sketching
3.6
A Summary of Curve Sketching
Pay attention or you won’t know which way to turn!

2. none
y-int. ( , )
x-int. ( , )
Domain:
Asymptote(s)
x = 0
H.A.
= 2

3. inc.
inc.
C.N. 0
1st der. test
no extrema
C.N. 0 up
down
Inf. pt.
none
2nd der. test
f”(0) = undefined
no extrema
Now let’s graph the given information.

4. x = 0
y = 2
Symmetry?
none

5. y-int. ( , )
(x-2)(x+1)
x-int. ( , )
Domain:
Asymptote(s)
x = -1
x = 2
H.A. y = 0
b/c degree of
N < degree of D
= 0

6. C.N. -1, 2 (x – 2)(x + 1) dec. -1 2 dec. dec. 1st der. (-1, ) (2, )
dec.
dec.
1st der. (-1, ) (2, )
no min.
or max.’s

7. C.N.’s .33, -1, 2
down up
down up
Inf. pt.s
(-1, ) (.33, ) (2, )
-.15
2nd der. test
Use –1 and 2 from 1st der.
f”(-1)
f”(2)
both are undefined, hence, no min’s or max’s
Now let’s graph.

8. x = -1
x = 2
Symmetry?
none

9. (x-2)(x+1)
Asymptote(s)
V.A.
@ x = 1
Slant asym.
y-int. ( , )
y = x
x-int. ( , )
( , )
2 0
-1 0
Domain:

10. C.N. 1 1
inc.
inc.
1st der. test = none up 1
down
C.N. 1
no inf. pt.
f”test at 1 fails

11. x = 1
Symmetry?
none
y = x