Questions: State whether the following rule defines y as a function of x or not. x 80 15 0 -1 0 15 80 y 9 4 1 0 -1 -4 -9 Is y a function of x? A. No, because at least one y-value of the given rule corresponds to more than one x-value. B. No, because at least one x-value of the given rule corresponds to more than one y-value. C. Yes, because each x-value of the given rule corresponds to exactly one y-value. D. Yes, because each y-value of the given rule corresponds to exactly one x-value.

State whether the following rule defines y as a function of x or not. x 80 15 0 -1 0 15 80 y 9 4 1 0 -1 -4 -9 Is y a function of x? A. No, because at least one y-value of the given rule corresponds to more than one x-value. B. No, because at least one x-value of the given rule corresponds to more than one y-value. C. Yes, because each x-value of the given rule corresponds to exactly one y-value. D. Yes, because each y-value of the given rule corresponds to exactly one x-value.

Solution

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Solution Steps

Step 1: Check for Unique $x$-values

We found that the $x$-value $x = 0$ corresponds to more than one $y$-value.

Step 2: Identify Repeated $x$-values

Since $x = 0$ maps to different $y$-values, it violates the definition of a function.

Final Answer:

The given rule does ^not^ define $y$ as a function of $x$ because $x = 0$ corresponds to multiple $y$-values.

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