Sketch the following on_a_graph Domain: (-0, –1) U (-1,1) U (1, 00) Intercepts:(0,0) Symmetry: symmetry with respect to the y-axis (even symmetry; i.e.,f(-x) = f(x) Asymptotes: Vertical at x = 1, x = -1; Horizontal at y = 1 Intervals of increasing/decreasing: f ↑ on (-∞,-1) U (-1,0); f 1 on (0,1) U (1, 0) Relative Extrema: Rel. max at (0,0) Concavity: f is concave up on (–∞, -1) U (1, 0) and f is concave down on (-1,1) Point of inflection: None

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Sketch the following on a_graph
Domain: (-0, –1) U (–1,1) U (1, o)
Intercepts: (0,0)
Symmetry: symmetry with respect to the y-axis (even symmetry; i.e.,f(-x) = f (x)
Asymptotes: Vertical at x = 1, x = -1; Horizontal at y = 1
Intervals of increasing/decreasing: f ↑ on (-∞,–1)U(-1,0); f 1 on (0,1) U (1, 0)
Relative Extrema: Rel. max at (0,0)
Concavity: f is concave up on (-∞, -1) U (1, 0) and f is concave down on (-1,1)
Point of inflection: None
Transcribed Image Text:Sketch the following on a_graph Domain: (-0, –1) U (–1,1) U (1, o) Intercepts: (0,0) Symmetry: symmetry with respect to the y-axis (even symmetry; i.e.,f(-x) = f (x) Asymptotes: Vertical at x = 1, x = -1; Horizontal at y = 1 Intervals of increasing/decreasing: f ↑ on (-∞,–1)U(-1,0); f 1 on (0,1) U (1, 0) Relative Extrema: Rel. max at (0,0) Concavity: f is concave up on (-∞, -1) U (1, 0) and f is concave down on (-1,1) Point of inflection: None
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