when does a range and domain equal a function

[concerro]

{2,3} {2,1} {2,4} {3,1} {3,2} {3,4}

According to this example I would say not because the the range has different values.

I have looked on various websites, but they seem to over complicate things. I am under the impression that if as the above statement goes if the ordered pairs don't have the same y value(range) it is not a function. Is that correct?

 

[Deleted member 4993]

{2,3} {2,1} {2,4} {3,1} {3,2} {3,4}

According to this example I would say not because the the range has different values.

I have looked on various websites, but they seem to over complicate things. I am under the impression that if as the above statement goes if the ordered pairs don't have the same y value(range) it is not a function. Is that correct?

I am not sure what do you mean by your statement.

Range and domain are properties of a function.

It is like saying the perfume and the color equal a flower.

 

[concerro]

This is copied from this page--> http://www.purplemath.com/modules/fcns2.htm

State the domain and range of the following relation. Is the relation a function?
{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

The above list of points, being a relationship between certain x's and certain y's, is a relation. The domain is all the x-values, and the range is all the y-values. To give the domain and the range, I just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(It is customary to list these values in numerical order, but it is not required. Sets are called "unordered lists", so you can list the numbers in any order you feel like. Just don't duplicate: technically, repititions are okay in sets, but most instructors would count off for this.)

While the given set does represent a relation (because x's and y's are being related to each other), they gave me two points with the same x-value: (2, –3) and (2, 3). Since x = 2 gives me two possible destinations, then this relation is not a function.

Note that all I had to do to check whether the relation was a function was to look for duplicate x-values. If you find a duplicate x-value, then the different y-values mean that you do not have a function.

The bolded area is the area I don't understand. What numbers have to be different to make it not a function?

 

[wjm11]

{2,3} {2,1} {2,4} {3,1} {3,2} {3,4}

“Note that all I had to do to check whether the relation was a function was to look for duplicate x-values. If you find a duplicate x-value, then the different y-values mean that you do not have a function.”

The bolded area is the area I don't understand.

Here is a very simple way to understand: if you plot the points on an xy-graph and one of the points is straight above another, then it’s NOT a function.

This is known as the “vertical line test.” It means if you pass a vertical line across your graph, it can only touch one point at a time for it to be a function. If it touches more than one point at a time anywhere on the graph, then it’s NOT a function.

Notice that in your list, you have two ordered pairs that have the same x value, {2,3} and {2,4}. One point is directly above the other, so they fail the vertical line test. This is NOT a function.

Hope that helps.

 

[concerro]

Thanks, I understand now.