(Section 1.2: Graphs of Functions) 1.2.6 PART E: IMPLICIT FUNCTIONS and CIRCLESExample 3 (An Equation that Describes a Function Implicitly)The equation xy=1implicitlydescribes yas a function of x. This is because, if we solve the equation for y, we obtain: y=1x. This is of the form y=fx(), wherefis the reciprocal function. §Example 4 (Implicit Functions and Circles; Revisiting Example 2)As it stands, the equation x2+y2=9does notdescribe yas a function of x; we saw this in Example 2. However, it doesprovide implicit functionsif we impose restrictions on xand/or yand consider smaller pieces of its graph.
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