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# Sec12.1 - Sec.12.1 Functions of Several Variables A...

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Sec.12.1 Functions of Several Variables A function f of two variables is a rule that assigns to each ordered pair of real numbers (x, y) in a set D a unique real number denoted by f(x, y) . The set D is the domain of f and its range is the set of values that f takes on. If f is a function of two variables with domain D, then the graph of f is the set of all points (x, y, z ) in Real 3 space such that z = f(x,y) and ( x,y ) is in D. A linear function of two variables is of the form z = f(x,y) = ax + by + c and graphs the plane ax + by –z + c = 0. EX 1 Sketch the graph of z = 12 -4x -3y . Since the function graphs a plane, choose the intercepts to graph. x y z = f(x, y) 0 0 x intercept 0 0 y intercept 0 0 z intercept EX 2 Let (, ) l n ( 1 ) fxy x y =+ . A. Evaluate f(1, 1) and f(e, 1). B. Find and sketch the domain of f . C. Find the range of f .

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The level curves or contour curves of a function f of two variables are the curves with the equations
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Sec12.1 - Sec.12.1 Functions of Several Variables A...

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