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