Question

How do you determine if the following sets of points is a function:$\\{ (2,3)( - 1,3)(4,7)( - 1,5)\\} ?$

Answer 1

For the given problem, first we are writing each point of sets in the form of $x$ and $y$ then we are going to observe each obtained value of $x$ and $y$ in such a way that for each input value of $x$ what will be the output value of $y$. If we get two distinct output values of $y$ for the same input value of $x$ then we are able to conclude that given points are not the points of any function it can only be said as relation points.

Complete step by step solution:
First, writing each point as $x$and $y$ as following,
$x = 2$, $y = 3$
$x = - 1$, $y = 3$
$x = 4$, $y = 7$
$x = - 1$, $y = 5$
Observing each point and writing it as following,
For input value of 2, the output value is 3
For input value of -1, the output value is 3
For input value of 4, the output value is 7
For input value of -1, the output value is 5
From the above observation it can be clearly seen that for the same input value of $x = - 1$ we are getting two distinct values of $y$ as $3$ and $5$. So, it would never be possible for any function that for a single input value of $x$ we get two distinct values of $y$.
Finally, we are in a position to say that given sets of points are not the points of function but only can be called as some relation.
Hence, given sets of points are points of relation not function.

Note:
In the above given set of points the first digit is always considered as $x$ value and the second one is $y$ value.