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
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.