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

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.