A SUMMARY OF CURVE SKETCHING Section 3.6. When you are done with your homework, you should be able...
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Transcript of A SUMMARY OF CURVE SKETCHING Section 3.6. When you are done with your homework, you should be able...
A SUMMARY OF CURVE SKETCHING
A SUMMARY OF CURVE SKETCHING
Section 3.6
When you are done with your homework, you should
be able to…
Analyze and sketch the graph of a function.
Diophantus lived in 300AD. He was the most famous algebraist of the ancient
world. He started the subject of Diophantine Analysis. This is the study
of…
A. Trigonometry.B. Physics.C. Integer solutions to equations.D. Probability.
GUIDELINES FOR ANALYZING THE GRAPH OF A FUNCTION
1. Determine the domain and range of the function.
2. Determine the intercepts of the graph.3. Determine the asymptotes of the
graph.4. Determine the symmetry of the graph.5. Locate the x-values for which and
either are 0 or do not exist. Use these results to determine relative extrema, concavity, and points of inflection.
f x f x
EXAMPLE: DISCUSS AND SKETCH THE GRAPH OF
Step 1: Find domain
Step 2: Find Intercepts
Step 3: Find Asymptotes.
2 1
xy
x
EXAMPLE (CONTINUED): DISCUSS AND SKETCH THE
GRAPH OF
Step 4: Symmetry
Step 5: Find critical values for f and f’
2 1
xy
x
DISCUSSION…Input value
or open interval
Conclusiony y y
2 1
xy
x
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