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 see 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 of 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 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.

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0. Fundamental Concepts of Algebra3h 32m
1. Equations and Inequalities3h 27m
2. Graphs1h 43m
3. Functions & Graphs2h 17m
4. Polynomial Functions1h 54m
5. Rational Functions1h 23m
6. Exponential and Logarithmic Functions2h 28m
7. Measuring Angles40m
8. Trigonometric Functions on Right Triangles2h 5m
9. Unit Circle1h 19m
10. Graphing Trigonometric Functions1h 19m
11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
12. Trigonometric Identities 2h 34m
13. Non-Right Triangles1h 38m
14. Vectors2h 25m
15. Polar Equations2h 5m
16. Parametric Equations1h 6m
17. Graphing Complex Numbers1h 7m
18. Systems of Equations and Matrices3h 6m
19. Conic Sections2h 36m
20. Sequences, Series & Induction1h 15m
21. Combinatorics and Probability1h 45m
22. Limits & Continuity1h 49m
23. Intro to Derivatives & Area Under the Curve2h 9m

3. Functions & Graphs

Intro to Functions & Their Graphs

Precalculus

3. Functions & Graphs

Intro to Functions & Their Graphs

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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

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Identify the set of ordered pairs given: {(2,5), (0,2), (2,9)}.

Determine the inputs (domain) from the ordered pairs. The inputs are the first elements of each pair: {2, 0}.

Determine the outputs (range) from the ordered pairs. The outputs are the second elements of each pair: {5, 2, 9}.

To determine if the relation is a function, check if each input is associated with exactly one output. In this case, the input '2' is associated with two different outputs: '5' and '9'.

Since the input '2' maps to more than one output, the relation is not a function.