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# 7.3 Curve Sketching .pdf

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Simon Fraser University

Mathematics

MATH 157

Chiaka Drake

Fall

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Chapter 7.3 Curve Sketching
Limits and one-Sided Limits of Infinity: If f (x)
becomes ______________ large in __________________
(positive or negative) as x approaches the number a from
the left side, then the limit does _____ exist , but we can
write lim f (x) or lim f (x) . Similarly for
x a x a
right side, lim f (x) or lim f (x) .
x a x a
Note 1: The line x a is a _____________ asymptote of
the curve y f (x) if at least one of the following is true:
xlia f (x) xia f (x) lxmaf (x)
lim f (x) lim f (x) lim f (x)
x a x a x a Example
2x,x 3
Q1: Given f (x) 4 , find the following limits,
x 5 ,x 3
if they exist:
a) xi5 f (x)
b) lim f (x)
x 5
c) lim f (x)
x 5 3
RECALL – Horizontal Asymptotes: If xim f (x) L,
then _______ is a horizontal asymptote . Similarly, if
xlim f (x) M , then _______ is a horizontal asymptote .
Curve Sketching Guidelines: I suggest you do the
following steps in ____________ in order to sketch the
graph of a function f .
1. Determine the __________, and where the function is
____________.
2. Find all ____________. Graph them, if any.
3. Determine if there are any ____________ asymptotes
(x ,x ). Graph them, if any.
4. Determine if there are any ____________ asymptotes
(x undefined place ). Graph them, if any.
5. Find f . 4
6. Find the ____________ numbers c ,c ,... 1f 2 and
all x-values where f is ____________ u ,u ,...1 Us2
these numbers to make a ________ for f and f .
7. Apply the ____________ Test to determine intervals
of ____________ and ____________.
8. Apply the ________ Derivative Test to determine
____________ and ____________ points. Graph
them, if any. Add max, min mini-sketch: .
9. Find f .
10. Find the ____________ numbers c ,c ,... 1f 2 and
all x-values where f is ____________ u ,u ,...1 Us2
these numbers to make a ________ for f and f.
11. Apply the ____________ Test to determine intervals
of ____________ and ____________.
12. Find all ____________ points. Graph them, if any.
Add inflection mini-sketch according to concavity
table: .
13. Use both ________ to complete the sketch of the
graph and don’t forget to ________ the graph f . 5
Examples
Q2:

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