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Graphing Rational Functions. Example (1) For the following function: determine the intervals of increase/decrease, the intervals of upward/downward concavity,

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Presentation on theme: "Graphing Rational Functions. Example (1) For the following function: determine the intervals of increase/decrease, the intervals of upward/downward concavity,"— Presentation transcript:

1 Graphing Rational Functions

2 Example (1) For the following function: determine the intervals of increase/decrease, the intervals of upward/downward concavity, the points of extremum and inflection, the intersections with the axes and the asymptotes and then graph it.

3 Asymptotes

4 Intersection with the Axes & Extremum See Appendix

5 Intervals of increase/decrease

6 Another Way to show extremum First Derivative Test

7 Concavity

8 Graph

9 Example (2) For the following function: determine the intervals of increase/decrease, the intervals of upward/downward concavity, the points of extremum and inflection, the intersections with the axes and the asymptotes and then graph it.

10 Asymptotes

11 Intersection with the Axes & Extremum See Appendix

12 Intervals of increase/decrease

13 Another Way to show extremum First Derivative Test

14 Concavity

15 Graph

16 Example (3) For the following function: determine the intervals of increase/decrease, the intervals of upward/downward concavity, the points of extremum and inflection, the intersections with the axes and the asymptotes and then graph it.

17 Asymptotes

18 Intersection with the Axes & Extremum See Appendix

19 Intervals of increase/decrease

20 Another Way to show extremum First Derivative Test

21 Concavity

22 Graph

23 Appendix Differentiating & Simplifying

24 Example(1)

25

26 Example(2)

27

28 Example(3)

29

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