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Unformatted text preview: Section 4.4: Curve Sketching To sketch a curve y = f ( x ), first identify: A. Domain B. Intercepts C. Symmetry (and periodicity) D. Asymptotes (vertical, horizontal, or slant) (See exercises 4.4.47-50: We say y = L ( x ) := mx + b is a slant asymptote to y = f ( x ) if f ( x ) – L ( x ) → 0 as x → ∞ or as x → – ∞ .) E. Intervals of increase or decrease F. Local maximum and minimum values G. Intervals of upward/downward concavity and points of inflection Then H. Sketch the curve! Apply to problem 25: f ( x )= x +sqrt(| x |). A. Domain is R (aka (– ∞ , ∞ )). B. Intercepts are (0,0) and (–1,0). C. Symmetry/periodicity: None. D. Asymptotes? ..?.. lim x →∞ ( x +sqrt(| x |)) = ∞ , lim x → – ∞ ( x +sqrt(| x |)) = – ∞ . No asymptote. (Is y = x a slant asymptote? ..?.. No, because the difference between x +sqrt(| x |) and x does not go to 0 as x →∞ or as x → – ∞ .) E. Intervals of increase or decrease....
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