A Summary of Curve Sketching

1
3.6 A Summary of Curve Sketching
Pay attention or you wont know which way to turn!
2
none
y-int. ( , )
x-int. ( , )
Domain
Asymptote(s)
V.A. _at_ x 0
H.A.
2
3
inc.
inc.
0
C.N. 0
1st der. test
no extrema
C.N. 0
0
up
down
Inf. pt.
none
2nd der. test
f(0) undefined
no extrema
Now lets graph the given information.
4
x 0
y 2
Symmetry?
none
5
0 0
y-int. ( , )
(x-2)(x1)
x-int. ( , )
0 0
Domain
Asymptote(s)
V.A. _at_ x -1 x 2
H.A. y 0 b/c degree of N lt degree of D
0
6
C.N. -1, 2
(x 2)(x 1)
-1 2
dec.
dec.
dec.
1st der. (-1, ) (2, )
no min. or max.s
7
C.N.s .33, -1, 2
-1 .33 2
down
down
up
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 mins or maxs
Now lets graph.
8
x -1
x 2
Symmetry?
none
9
(x-2)(x1)
Asymptote(s)
V.A.
_at_ x 1
Slant asym.
y x
y-int. ( , )
0 2
x-int. ( , ) ( , )
2 0 -1 0
Domain
10
C.N. 1
1
inc.
inc.
1st der. test none
up
down
1
C.N. 1
no inf. pt.
ftest at 1 fails
11
x 1
Symmetry?
none
y x