A SUMMARY OF CURVE SKETCHING

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A SUMMARY OF CURVE SKETCHING

• Section 3.6

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When you are done with your homework, you should
be able to

• Analyze and sketch the graph of a function.
•  

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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

1. Trigonometry.
2. Physics.
3. Integer solutions to equations.
4. Probability.

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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.

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EXAMPLE DISCUSS AND SKETCH THE GRAPH OF

• Step 1 Find domain
• Step 2 Find Intercepts
• Step 3 Find Asymptotes.

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EXAMPLE (CONTINUED) DISCUSS AND SKETCH THE
GRAPH OF

• Step 4 Symmetry
• Step 5 Find critical values for f and f

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DISCUSSION
Input value or open interval Conclusion











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