Question 1163159
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(d)  2*|x| = y.


     This formula express y as a function of x

         y = 2*|x|.     (d)

     For every value of x, formula (d) determines y by a unique way.

     In other words, for any real x as an input, formula (d) determines a unique output y.


     <U>By the definition of the notion of a function</U>, it means that formula (d)  determines y as a function of x.




(b)  Same mantra works in case (b).


     You start from the formula

         x^2 + y = 100.


     It defines the expression

         y = 100 - x^2.     (b)


     For every value of x, the formula (b) determines y by a unique way.

     In other words, for any real x as an input, formula (b) determines a unique output y.


     <U>By the definition of the notion of a function</U>, it means that formula (b)  determines y as a function of x.




(a)  Same mantra works in case (a).


     You start from the formula

         x + 5y = 15.


     It defines the expression

         y = {{{(15-x)/5}}}.     (a)


     For every value of x, formula (a) determines y by a unique way.

     In other words, for any real x as an input, formula (a) determines a unique output y.


     <U>By the definition of the notion of a function</U>, it means that formula (a)  determines y as a function of x.




(c)  Same mantra DOES NOT work in case (c).


     You start from the formula

         x^2 + y^2 = 100.


     It defines the expression

         y = +/- {{{sqrt(100-x^2)}}}.     (c)


     Formula (c) DOES NOT determine y by a unique way.

     In opposite, to each value of x  between -10 and 10,  -10 < x < 10,  formula (c) determines TWO values of y.

     In other words, for any real x as an input, formula (c) determines TWO DIFFERENT outputs y.


     <U>By the definition of the notion of a function</U>, it means that formula (c)  DOES NOT determine y as a function of x.


     In this case, y is not a function of x.
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