Consider the function f(x, y) = xy, for x ≥ 0 and y ≥ 0.                                       (a) Sketch the graph of the surface given by f.                                               (b) Make a conjecture about the relationship between the graphs of f and g(x, y) = f(x, y) − 3. Explain your reasoning.                                                        (c) Repeat part (b) for g(x, y) = −f(x, y).                                                            (d) Repeat part (b) for g(x, y) = 1/2 f(x, y).                                                            (e) On the surface in part (a), sketch the graph of z = f(x, x).

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the function f(x, y) = xy, for x ≥ 0 and y ≥ 0.                                       (a) Sketch the graph of the surface given by f.                                               (b) Make a conjecture about the relationship between the graphs of f and g(x, y) = f(x, y) − 3. Explain your reasoning.                                                        (c) Repeat part (b) for g(x, y) = −f(x, y).                                                            (d) Repeat part (b) for g(x, y) = 1/2 f(x, y).                                                            (e) On the surface in part (a), sketch the graph of z = f(x, x).

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