Question
What is the largest value of x that would make the following list of a points not a function.
(__,12),(3,17),(17,21)
(__,12),(3,17),(17,21)
Answers
GPT-4o mini
A relation is not a function if at least one x-value corresponds to more than one y-value. In the provided list of points:
- \((__,12)\)
- \((3,17)\)
- \((17,21)\)
To determine which value of \(x\) would make the relation not a function, we need to look at the first component of the point with the missing \(x\) value.
If we assign \(x\) of the missing point to be any value that is not already used in other points (in this case, 3 and 17), it will not create a situation where a single x-value maps to multiple y-values.
The points we have currently:
- At \(x = 3\), the \(y\) value is 17.
- At \(x = 17\), the \(y\) value is 21.
The largest \(x\) value we can assign to the missing point is \(17\) (the maximum \(x\) used in the points). However, using \(17\) would create a conflict, as two points would then have the same \(x\) value (both \(x = 17\) would yield different \(y\) values).
Thus, assigning the largest possible value for the missing \(x\) to \(17\) would result in the relation not being a function. Therefore, the largest value of \(x\) that would make the relation not a function is:
\[
\boxed{17}
\]
- \((__,12)\)
- \((3,17)\)
- \((17,21)\)
To determine which value of \(x\) would make the relation not a function, we need to look at the first component of the point with the missing \(x\) value.
If we assign \(x\) of the missing point to be any value that is not already used in other points (in this case, 3 and 17), it will not create a situation where a single x-value maps to multiple y-values.
The points we have currently:
- At \(x = 3\), the \(y\) value is 17.
- At \(x = 17\), the \(y\) value is 21.
The largest \(x\) value we can assign to the missing point is \(17\) (the maximum \(x\) used in the points). However, using \(17\) would create a conflict, as two points would then have the same \(x\) value (both \(x = 17\) would yield different \(y\) values).
Thus, assigning the largest possible value for the missing \(x\) to \(17\) would result in the relation not being a function. Therefore, the largest value of \(x\) that would make the relation not a function is:
\[
\boxed{17}
\]