14209an5b.1-3

14209an5b.1-3 - c Kendra Kilmer March 26, 2009 Section 5.4...

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Unformatted text preview: c Kendra Kilmer March 26, 2009 Section 5.4 - Curve Sketching Techniques Graphing Strategy: Step 1: Analyze f (x) Find the domain of f . Find the intercepts. Find asymptotes. Step 2: Analyze f (x): Create sign chart for f (x) and determine intervals of increasing/decreasing and local extrema. Step 3: Anlayze f (x): Create sign chart for f (x) and determine intervals of concave up, concave down, and inflection points. Step 4: Sketch the graph of f using all of the above information. Plot additional points as needed. 2+x . 3-x Example 1: Use the graphing strategy to sketch a graph of f (x) = 1 c Kendra Kilmer March 26, 2009 2x2 + 11x + 14 Example 2: Use the graphing strategy to sketch a graph of f (x) = . x2 - 4 2 c Kendra Kilmer March 26, 2009 Example 3: Use the graphing strategy to sketch a graph of f (x) = (x - 2)ex . Example 4: Use the given information to sketch the graph of f . Domain: (-, -1) (-1, 1) (1, ) Asymptotes: x = -1, x = 1, y = 0 f (-2) = 1, f (0) = 0, f (2) = 1 f (x) > 0 on (-, -1) (0, 1) f (x) < 0 on (-1, 0) (1, ) f (x) > 0 on (-, -1) (-1, 1) (1) Section 5.4 Homework Problems: 1,5,9,13,17,21,29,37,41,45,53,67,77 and supplemental problems 3 ...
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14209an5b.1-3 - c Kendra Kilmer March 26, 2009 Section 5.4...

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