QQuestionMathematics
QuestionMathematics
Which relation is a function? A.
| $x$ | $y$ |
| --- | --- |
| 4 | - 2 |
| 5 | - 3 |
| 6 | - 2 |
| 7 | - 3 |
B.
| $x$ | $y$ |
| --- | --- |
| 3 | 10 |
| 2 | 20 |
| 3 | 30 |
| 4 | 40 |
C.
| $x$ | $y$ |
| --- | --- |
| - 5 | 2 |
| - 5 | 3 |
| - 10 | 4 |
| - 10 | 5 |
D.
| $x$ | $y$ |
| --- | --- |
| 10 | 15 |
| 20 | 25 |
| 8 | 30 |
| 20 | 35 |
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Answer
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Step 1:: Identify the relations that are functions by checking if each x-value corresponds to only one y-value.
Step 2:: Analyzing option A, we see that x = 4, 5, 6, and 7 correspond to y = - 2, - 3, - 2, and - 3, respectively.
Since the x-value 4 corresponds to y = - 2 and - 3, this relation is not a function. We can eliminate option A.
Step 3:: For option B, x = 3 corresponds to y = 10 and 30, but the other x-values (2 and 4) correspond to only one y-value each.
Thus, this relation is a function.
Step 4:: In option C, x = - 5 corresponds to both y = 2 and 3, so this relation is not a function.
We can eliminate option C.
Step 5:: Lastly, for option D, x = 10 and 20 correspond to more than one y-value.
So, this relation is not a function.
Step 6:: Of the given options, only option B is a function.
Final Answer
The relation in option B is a function.
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