Name:_________________________
Calculus 3.6 Guided Notes
A Summary of Curve Sketching
So far this year we have learned/reviews all the techniques it takes to effectively sketch an accurate
graph with all critical points located. Here is a list of the following steps you should take in order to
sketch a graph correctly.
Step
1
2
3
4
5
6
7
8
9
10
11
Find
x-intercepts and y-intercepts
Symmetry
Domain and Range
Continuity
Vertical Asymptotes
Differentiability
Relative Extrema
Concavity
Points of Inflection
Horizontal Asymptotes
Infinite Limits at Infinity
Section in Book
P.1
P.1
P.3
1.4
1.5
2.1
3.1
3.4
3.4
3.5
3.5
Sketch a graph with the following information.
F(x)
-∞ < x < -2
x = -2
-2 < x < 0
x=0
0<x<2
x=2
2<x<∞
F’(x)
UND UND
9/2 0
+
UND UND
F”(x)
UND
+
+
+
UND
Characteristic of Graph
Sketch the graph, Find and label ALL important parts
1) f ( x) 
x 2  2x  4
x 2
Intercepts
y-int
x-int
lim 
x  
lim 
x 
Asymptotes
Vertical
f ' ( x) 
Horizontal
f ' ( x)
Extrema
min(s)
f " ( x) 
max(s)
f " ( x)
P.O.I(s)
Sketch the graph, Find and label ALL important parts
2) f ( x) 
x
x 2
2
Intercepts
y-int
x-int
lim 
x  
lim 
x 
Asymptotes
Vertical
f ' ( x) 
Horizontal
f ' ( x)
Extrema
min(s)
f " ( x) 
max(s)
f " ( x)
P.O.I(s)
Sketch the graph, Find and label ALL important parts
3) f ( x)  x x  4 
3
Intercepts
y-int
x-int
lim 
x  
lim 
x 
Asymptotes
Vertical
f ' ( x) 
Horizontal
f ' ( x)
Extrema
min(s)
f " ( x) 
max(s)
f " ( x)
P.O.I(s)