developing the graph of a function. 3. set up a number line with the critical points on it

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