Example: Is this relation a function?

We look at an example of a relation and decide whether it more specifically is a function. That is, does it obey the property that every single input has one corresponding output?

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This video was created by Dr. Trefor Bazett

[arslanahmed]

A relation is a general idea that connects pairs of values from two sets, allowing one input to be related to multiple outputs. For example, in the relation 𝑅={(1, 2), (1, 3), (2, 4)}, the input 1 is connected to both 2 and 3. On the other hand, a function is a special kind of relation where each input has exactly one output. For example, the function 𝑓(𝑥)=𝑥^2 gives one output for each input. The equation of a circle, 𝑥^2+𝑦^2=1, is a relation because some inputs can lead to multiple outputs (like 𝑦=1and 𝑦=−1 when x=0). Functions must pass the vertical line test on a graph, meaning a vertical line can only touch the graph at one point. Moreover, all functions are relations, but not all are functions because functions have stricter rules about how inputs and outputs are connected.

[marabi]

At 4:30 if you only consider the semi circle then shouldn't your restriction of open interval [-1, 1] to [-1, 1] be altered to [-1, 1] since you erased the bottom half of the graph, and therefore it is no longer part of our analysis ?

[uridimmuvltozwta]

could you say that if there is more than one variable it can not be a function? such 2x+3 can be a function because if put "2" in "x" you will always get 7. But 2x+y can not be a function because if you put "2" in "x" and "3" in "y" you get 7, but if you replace "y" with 4 now you get 8, even though the "x" did not change. Or is there a case where you can have one variable and it it not be a function, or a case where if you have more than one variable it can be a function?

[chintzzP]

I'm struggling to wrap my head around this. Surely if you just choose to ignore the bottom half, it still exists in terms of the equation, so saying it passes the vertical line test is incorrect?

[Kurtlane]

OK, so if the full circle thing is not a function, what is it called? It's not an equation, and calling it a relation sounds clumsy. There are all sorts of relations, ((2, 1) is a relation), but this is too close to a function to be just a relation.

Thanks.

[NoMeDigasALBERTO]

I think it's easier if we just solve the function for "y". y2 = 1 - x2 .... y1= √ 1 - x2 .... y2= -√ 1 - x2 ... So it's not a function, because we have 2 different values for "y". The graphic explanation is a bit confusing for me.

[kaungpyae]

I don't understand this lecture. Can someone help me to understand with any extra or more basic explanations?

[smonkey]

Please someone. Is this not a function? : `function getOne(int: x) { return 1; } `

[poenanster]

okay, I might be dumbass, but following the first rule of defining a function, you said that every x component has to have an output. Rule two dictates that it should only be a singular unique value of y for every x component, but thats not where my question lies. If rule one were to be respected, then technically speaking, a Tangent function, isn't one. Is it just me applying the wrong set of rules to non relavent arguments? please halp.

[labiribiri]

You blundered so hard this lecture. The last part of the circle example was extremely unnecessary and only brought confusion.

You only covered the first two rules in your example but you ignored the third.