Precalc0101to0102-page26 - (Section 1.2: Graphs of...

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(Section 1.2: Graphs of Functions) 1.2.6 PART E: IMPLICIT FUNCTIONS and CIRCLES Example 3 (An Equation that Describes a Function Implicitly) The equation xy = 1 implicitly describes y as a function of x . This is because, if we solve the equation for y , we obtain: y = 1 x . This is of the form y = fx () , where f is the reciprocal function. § Example 4 (Implicit Functions and Circles; Revisiting Example 2) As it stands, the equation x 2 + y 2 = 9 does not describe y as a function of x ; we saw this in Example 2. However, it does provide implicit functions if we impose restrictions on x and/or y and consider smaller pieces of its graph.
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This document was uploaded on 12/29/2011.

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