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Which representation does NOT show y as a function of x?

A. y=x^2
B. x=y^2
C. y= \sqrt(x)
D. x=2y+1

User Delrog
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1 Answer

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Final answer:

Option B, 'x=y²', is the correct answer as it does not show y as a function of x because a single x-value corresponds to two y-values, violating the definition of a function.

Step-by-step explanation:

The question asked is 'Which representation does NOT show y as a function of x?' To determine if y is a function of x, every x-value should correspond to exactly one y-value. In options A, C, and D, every x-value corresponds to a unique y-value, making y a function of x. However, in option B, 'x=y²', each positive x-value corresponds to two possible y-values (one positive and one negative), and thus y is not uniquely determined by x. This means that B does not represent y as a function of x.

Examples:

  • For A, y=x², if x=1, then y=1²=1.
  • For C, y=√(x), if x=4, then y=\sqrt(4)=2.
  • For D, x=2y+1, if y=2, then x=2(2)+1=5.

Hence, x=y² is the correct answer as it does not depict y as a function of x because it fails the Vertical Line Test in a graph representation, where a vertical line on the graph would intersect at two points, indicating that a single x-value has more than one corresponding y-value.

User Persis
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