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Developing the Graph of a Function

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

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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

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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

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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

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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

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Developing the Graph of a Function

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

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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

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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

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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

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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

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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

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Developing the Graph of a Function

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

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Developing the Graph of a Function

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3. Asymptotes occur where the denominator = 0

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

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

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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

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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

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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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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

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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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Use your knowledge of the derivative to describe the graph.

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