Function or Not?

mathdad

mathdad

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Apr 24, 2015
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Given the set of points (5, 10), (-4, 56), (5, 67), and (2, 78), do we have a function here?

I say no function because there are two x-values with 5.
 
mathdad said:
Given the set of points (5, 10), (-4, 56), (5, 67), and (2, 78), do we have a function here?

I say no function because there are two x-values with 5.
Click to expand...
Your logic is correct. The given expression fails the vertical line test.
 
mathdad said:
Given the set of points (5, 10), (-4, 56), (5, 67), and (2, 78), do we have a function here?

I say no function because there are two x-values with 5.
Click to expand...

It's important that y values are different in those 2 points.
 
mathdad said:
Why is it important for y values to be different in those two points?
Click to expand...
A relation is said to be a function if for each input (x-value) you get back back exactly one output (y-value)
If the same x-value appears twice and it has the same y-value (like (2,5), (2,5)), then this does not mean that you do not have a function.
The test for this type of problem is to look for x-values that has multiple y-value. If you find such points, then you do not have a function, if you do not have such points then you have a function.
 
Jomo said:
A relation is said to be a function if for each input (x-value) you get back back exactly one output (y-value)
If the same x-value appears twice and it has the same y-value (like (2,5), (2,5)), then this does not mean that you do not have a function.
The test for this type of problem is to look for x-values that has multiple y-value. If you find such points, then you do not have a function, if you do not have such points then you have a function.
Click to expand...

Given the set of points (5, 10), (7, 6), (6, 10), and (2, 78), do we have a function here?

Here, the points (5,10) and (6,10) have the same y-value. This is okay according to your reply. I am going to say that we have a function.
 
mathdad said:
Why is it important for y values to be different in those two points?
Click to expand...
One might answer that if is just part of the definition of a function.
But then you ask why is it a requirement.
Here is a folk-explanation. A function is a relation from one set to another. It is a special relation that relates each element of the first set to one and only one element of the second set.
 
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