State the inputs and outputs of the following relation. Is it a function? { ( 2 , 5 ) , ( 0 , 2 ) , ( 2 , 9 ) \left(2,5\right),\left(0,2\right),\left(2,9\right) ( 2 , 5 ) , ( 0 , 2 ) , ( 2 , 9 ) }

let's see if we can solve this problem. In this problem, we are told to state the inputs and outputs of the following relation, which looks like this. We're also asked to determine whether or not this relation is an example of a function. Now, what I'm first going to do is list out all of the inputs or x values and all of the outputs or y values for this relation. Now the x values correspond to the first coordinates that we have. And doing this in ascending order, I see that we have 2, and then we have 0. Actually, I should start with 0 because that's lower, and then we have 2. And I noticed that we have 2 twice, but I'm only gonna write it once in this bubble here. So these are all the inputs that we have. Now as for the outputs, these are going to be all the y values or coordinates that we have here. We'll start with 2, that's one of the y values. We also have 5, and then we have 9. So these are going to be the outputs and the inputs. Now to figure out how these are related, well, let's take a look at these points. So we can see here based on this point that 2 is related to 5. We can see from this point that 0 is related to 2, and we can see from this point that 2 is related to 9. Now is this an example of a function? Well, for something to be a function, each input can only have one output. And notice that we actually do break this rule because this 2 here is related to 5, but it's also related to 9. We have an input with more than 1 output, and because this happens, we would say that this is not a function. So whenever you see an input which has multiple outputs, then it is not an example of a function. So this is the relation, and it's not a function. Hopefully, you found this helpful.

0. Functions

Introduction to Functions

Business Calculus

0. Functions

Introduction to Functions

Struggling with Business Calculus?

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Multiple Choice

State the inputs and outputs of the following relation. Is it a function? { $\left(2,5\right),\left(0,2\right),\left(2,9\right)$ }

Input and Output Sets

Verified step by step guidance

Step 1: Identify the inputs and outputs from the given relation. The relation is {(2,5), (0,2), (2,9)}. Here, the inputs are {2, 0} and the outputs are {5, 2, 9}.

Step 2: Understand the definition of a function. A relation is a function if each input is associated with exactly one output. This means no input can map to more than one output.

Step 3: Analyze the relation. In the given relation, the input '2' is associated with two different outputs: '5' and '9'. This violates the definition of a function.

Step 4: Conclude whether the relation is a function. Since the input '2' maps to multiple outputs, the relation is NOT a function.

Step 5: Summarize the findings. The inputs are {2, 0}, the outputs are {5, 2, 9}, and the relation is not a function because one input maps to multiple outputs.