Question
What is the largest value of x that would make the following list of a points not a function.
{(_,14),(3,18),(13,19)}
{(_,14),(3,18),(13,19)}
Answers
GPT-4o mini
In order for a list of points to not represent a function, it must contain at least two points that have the same x-coordinate but different y-coordinates.
Given the points \((_, 14)\), \((3, 18)\), and \((13, 19)\), we need to determine the largest value of \(x\) that can go in place of the underscore `_` such that the list of points still does not represent a function.
To ensure that these points do not form a function, we can take a look at the x-coordinates. We are currently missing the x-coordinate of the first point, which we denote as \(x_1\) (replacing `_`).
1. If \(x_1 = 3\), then the points are \((3, 14)\), \((3, 18)\), and \((13, 19)\). Here, both \((3, 14)\) and \((3, 18)\) have the same x-coordinate (3) but different y-coordinates, which violates the definition of a function.
2. If \(x_1\) is any number other than 3 (e.g., 2, 10, or 13), then the list consists of distinct x-coordinates: \(x_1\), \(3\), and \(13\). In this case, it would represent a function.
To maximize \(x_1\) while still making the set of points not a function, we conclude that the largest value for \(x_1\) that would make the set of points not a function is \(x_1 = 3\).
Thus, the largest value of \(x\) that would make the list of points not a function is:
\[
\boxed{3}
\]
Given the points \((_, 14)\), \((3, 18)\), and \((13, 19)\), we need to determine the largest value of \(x\) that can go in place of the underscore `_` such that the list of points still does not represent a function.
To ensure that these points do not form a function, we can take a look at the x-coordinates. We are currently missing the x-coordinate of the first point, which we denote as \(x_1\) (replacing `_`).
1. If \(x_1 = 3\), then the points are \((3, 14)\), \((3, 18)\), and \((13, 19)\). Here, both \((3, 14)\) and \((3, 18)\) have the same x-coordinate (3) but different y-coordinates, which violates the definition of a function.
2. If \(x_1\) is any number other than 3 (e.g., 2, 10, or 13), then the list consists of distinct x-coordinates: \(x_1\), \(3\), and \(13\). In this case, it would represent a function.
To maximize \(x_1\) while still making the set of points not a function, we conclude that the largest value for \(x_1\) that would make the set of points not a function is \(x_1 = 3\).
Thus, the largest value of \(x\) that would make the list of points not a function is:
\[
\boxed{3}
\]