1. A SUMMARY OF CURVE SKETCHING Section 3.6

2. When you are done with your homework, you should be able to… Analyze and sketch the graph of a function.

3. 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.

4. 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.

5. EXAMPLE: DISCUSS AND SKETCH THE GRAPH OF Step 1: Find domain Step 2: Find Intercepts Step 3: Find Asymptotes.

6. EXAMPLE (CONTINUED): DISCUSS AND SKETCH THE GRAPH OF Step 4: Symmetry Step 5: Find critical values for f and f’

7. DISCUSSION… Input value or open interval Conclusion

9. I LIKE USING THE CLICKERS DURING CLASS. A.Strongly Agree B.Agree C.Disagree D.Strongly Disagree

10. I THINK YOU SHOULD USE THE CLICKERS NEXT SEMESTER. A.Strongly Agree B.Agree C.Disagree D.Strongly Disagree

11. I LIKE IT WHEN YOU WRITE USING THE COMPUTER INSTEAD OF THE WHITEBOARD. A.Strongly Agree B.Agree C.Disagree D.Strongly Disagree