1. Developing the Graph of a Function

6. 3. Set up a number line with the critical points on it

7. Developing the Graph of a Function 3. Set up a number line with the critical points on it 4. Now test values in each interval in the derivative and use the conditions above

8. Developing the Graph of a Function 3. Set up a number line with the critical points on it 4. Now test values in each interval in the derivative and use the conditions above - Positive so increasing, draw an arrow going up on a slant

9. Developing the Graph of a Function 3. Set up a number line with the critical points on it 4. Now test values in each interval in the derivative and use the conditions above - Negative so decreasing, draw an arrow going down on a slant

10. Developing the Graph of a Function 3. Set up a number line with the critical points on it 4. Now test values in each interval in the derivative and use the conditions above - Positive so increasing, draw an arrow going up on a slant

11. Developing the Graph of a Function

17. 3. Set up a number line with the critical points on it

18. Developing the Graph of a Function 3. Set up a number line with the critical points on it 4. Now test values in each interval in the derivative and use the conditions above

19. Developing the Graph of a Function 3. Set up a number line with the critical points on it 4. Now test values in each interval in the derivative and use the conditions above - Negative so decreasing, draw an arrow going down on a slant

20. Developing the Graph of a Function 3. Set up a number line with the critical points on it 4. Now test values in each interval in the derivative and use the conditions above - positive so increasing, draw an arrow going up on a slant

21. Developing the Graph of a Function 3. Set up a number line with the critical points on it 4. Now test values in each interval in the derivative and use the conditions above - Negative so decreasing, draw an arrow going down on a slant

22. Developing the Graph of a Function 3. Set up a number line with the critical points on it 4. Now test values in each interval in the derivative and use the conditions above - positive so increasing, draw an arrow going up on a slant

23. Developing the Graph of a Function

24. ** rational functions like this will not only have critical points we have to find, but could have vertical asymptotes included in the intervals

25. Developing the Graph of a Function

32. 3. Asymptotes occur where the denominator = 0

33. Developing the Graph of a Function 3. Asymptotes occur where the denominator = 0

34. Developing the Graph of a Function 3. Asymptotes occur where the denominator = 0

35. Developing the Graph of a Function 3. Asymptotes occur where the denominator = 0 4. Set up a number line with the critical points and asymptotes on it

36. Developing the Graph of a Function 3. Asymptotes occur where the denominator = 0 4. Set up a number line with the critical points and asymptotes on it 5. Test values in each interval in the derivative

37. Developing the Graph of a Function 3. Asymptotes occur where the denominator = 0 4. Set up a number line with the critical points and asymptotes on it 5. Test values in each interval in the derivative - Negative so decreasing

38. Developing the Graph of a Function 3. Asymptotes occur where the denominator = 0 4. Set up a number line with the critical points and asymptotes on it 5. Test values in each interval in the derivative - positive so increasing

39. Developing the Graph of a Function 3. Asymptotes occur where the denominator = 0 4. Set up a number line with the critical points and asymptotes on it 5. Test values in each interval in the derivative - negative so decreasing