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Does Equation Define y as a Function of x: Six Examples

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Wendy

Initially the definition of a function is reviewed. To determine if an equation defines y as a function of x, the equation is solved for y and then it is tested to see if each x value corresponds to at most one y value. If every xvalue yields one yvalue then the equation defines y as a function of x. If any xvalue yields 2 (or more) yvalues then the equation does NOT define y as a function of x. The equations analyzed are: (a) 2x+3y=1 (b) x+y^2=9 (c) y=sqrt(x+9) (d) x^2+y=9 (e) 2y5=abs(x) (f) abs(y)=3x+7

Timestamps
0:00 Introduction
1:32 2x+3y=1
3:10 x+y^2=9
4:50 y=sqrt(x+9)
6:00 x^2+y=9
7:24 2y5=abs(x)
8:59 abs(y)=3x+7

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