Let f(x) be a function with all of the following properties. Sketch a graph of y = f(x). Explain your reasoning. (a) f(-1) = 2, f(1) = 1, f(2) = 2. (b) lim f(x) = 3 and lim f (x) = -2. (c) f(x) has vertical asymptotes at x = -2,0. (d) f'(x) > 0 on (-1,0) and (1,+0). f'(x) < 0 on (-0o, -2), (-2, –1), and (0, 1). (e) f"(x) > 0 on (-2,0) and (0, 2). f"(x) < 0 on (-0, -2) and (2, +0). く

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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.