Developing the Graph of a Function. 3. Set up a number line with the critical points on it.
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Transcript of Developing the Graph of a Function. 3. Set up a number line with the critical points on it.
![Page 1: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/1.jpg)
Developing the Graph of a Function
![Page 2: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/2.jpg)
Developing the Graph of a Function
![Page 3: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/3.jpg)
Developing the Graph of a Function
![Page 4: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/4.jpg)
Developing the Graph of a Function
![Page 5: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/5.jpg)
Developing the Graph of a Function
![Page 6: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/6.jpg)
Developing the Graph of a Function
3. Set up a number line with the critical points on it
![Page 7: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/7.jpg)
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
![Page 8: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/8.jpg)
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
![Page 9: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/9.jpg)
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
![Page 10: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/10.jpg)
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
![Page 11: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/11.jpg)
Developing the Graph of a Function
![Page 12: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/12.jpg)
Developing the Graph of a Function
![Page 13: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/13.jpg)
Developing the Graph of a Function
![Page 14: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/14.jpg)
Developing the Graph of a Function
![Page 15: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/15.jpg)
Developing the Graph of a Function
![Page 16: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/16.jpg)
Developing the Graph of a Function
![Page 17: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/17.jpg)
Developing the Graph of a Function
3. Set up a number line with the critical points on it
![Page 18: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/18.jpg)
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
![Page 19: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/19.jpg)
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
![Page 20: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/20.jpg)
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
![Page 21: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/21.jpg)
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
![Page 22: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/22.jpg)
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
![Page 23: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/23.jpg)
Developing the Graph of a Function
![Page 24: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/24.jpg)
Developing the Graph of a Function
** rational functions like this will not only have critical points we have to find, but could have vertical asymptotes included in the intervals
![Page 25: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/25.jpg)
Developing the Graph of a Function
![Page 26: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/26.jpg)
Developing the Graph of a Function
![Page 27: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/27.jpg)
Developing the Graph of a Function
![Page 28: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/28.jpg)
Developing the Graph of a Function
![Page 29: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/29.jpg)
Developing the Graph of a Function
![Page 30: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/30.jpg)
Developing the Graph of a Function
![Page 31: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/31.jpg)
Developing the Graph of a Function
![Page 32: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/32.jpg)
Developing the Graph of a Function
3. Asymptotes occur where the denominator = 0
![Page 33: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/33.jpg)
Developing the Graph of a Function
3. Asymptotes occur where the denominator = 0
![Page 34: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/34.jpg)
Developing the Graph of a Function
3. Asymptotes occur where the denominator = 0
![Page 35: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/35.jpg)
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
![Page 36: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/36.jpg)
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
![Page 37: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/37.jpg)
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
![Page 38: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/38.jpg)
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
![Page 39: Developing the Graph of a Function. 3. Set up a number line with the critical points on it.](https://reader035.fdocuments.net/reader035/viewer/2022081518/551b281b5503462e578b66e2/html5/thumbnails/39.jpg)
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