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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