Curve Sketching Example

AP Calculus · Axiom Academy

Example Curve Sketching Example Complete analysis of a rational function Domain: all . The only intercept is (0, 0) . Vertical: x = 2 and x = -2 . Horizontal: y = 2 (leading coefficients). f'(x) = 0 when x = 0 . Since f' changes from positive to negative at x = 0 &mdash, 'Apple Color Emoji', 'Segoe UI Emoji', 'Noto Color Emoji'; local maximum at (0, 0) . Analyzing f''(x) shows the function is concave up on and , concave down on (-2, 2) . The graph has three pieces: concave up approaching y=2 from above for x 2 . What is the horizontal asymptote of ? You've worked through the full solution. Review each step to solidify your understanding.

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