In which of the following is y a function of x?I. y2=9−x2II. ∣y∣=xIII. y=x23 I. y 2 =9−x 2 II. ∣y∣=xIII. y= 3 x 2
Question
In which of the following is y a function of x?I. y2=9−x2II. ∣y∣=xIII. y=x23 I. y 2 =9−x 2 II. ∣y∣=xIII. y= 3 x 2
Solution
I. y^2 = 9 - x^2 This is not a function of x because for each value of x, there are two possible values of y (one positive and one negative).
II. |y| = x This is also not a function of x because for each positive value of x, there are two possible values of y (one positive and one negative).
III. y = x^2/3 This is a function of x because for each value of x, there is exactly one corresponding value of y.
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