1. Let f be a function satisfying the following properties: • continuous on R\{1} • f(0) = 0 and f(3) = 7 • lim f(x) = +o lim [f(x) – (x + 2)] = 0 lim [f(x) – (x + 2)] = 0 Moreover, the table of signs for f' and f" is given below. (-∞0, 0) | 0 | (0, 1) 1 (1,3) | 3 | (3,+∞ f'(r) f"(x) + + und. + + und. + + 1. Give equations of the two linear asymptotes of the graph of f. 2. Determine where is f increasing or decreasing and concave up or concave down. Determine the relative maximum, relative minimum and inflection points of the graph of f (if any). 3. Sketch the graph of f with emphasis on concavity. Label all the relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective equations.

1. Let f be a function satisfying the following properties: • continuous on R\{1} • f(0) = 0 and f(3) = 7 • lim f(x) = +o lim [f(x) – (x + 2)] = 0 lim [f(x) – (x + 2)] = 0 Moreover, the table of signs for f' and f" is given below. (-∞0, 0) | 0 | (0, 1) 1 (1,3) | 3 | (3,+∞ f'(r) f"(x) + + und. + + und. + + 1. Give equations of the two linear asymptotes of the graph of f. 2. Determine where is f increasing or decreasing and concave up or concave down. Determine the relative maximum, relative minimum and inflection points of the graph of f (if any). 3. Sketch the graph of f with emphasis on concavity. Label all the relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective equations.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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