Question

Which table shows a function whose range has exactly three elements?

x |f(x)
1 | 4
2 | 4
3 | 4

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x |f(x)
3 | 8
4 | 6
5 | 12
6 | 8

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x |f(x)
0 | 5
2 | 9
0 | 15

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x |f(x)
1 | 4
3 | 2
5 | 1
3 | 4

Is the answer C? Help!

Answer 1

@ganeshie8

Answer 2

To me it seems that options B, C, and D are all correct answers.

Answer 3

There is only one option that will be correct, which one do you think is best? I assume three elements means that everything has to be different.

Answer 4

The range is the set of y-coordinates.

Every point in option A has y-coordinate 4, so the range is the set {4}. This set has only 1 element.

In option B, the y-coordinates are 8, 6, 12, and 8. All those y-coordinates are in the set {6, 8, 12}. This set has 3 elements. This is why I say option B is a correct answer. The fact that the 12 appears twice does not change the range since each number appears in a set only once.

Skipping to option D, you have a similar situation with y-coordinates 4, 2, 1, 4. Once again, just because 4 appears twice, the set containing the y-coordinates, which is the range, is {1, 2, 4}. This set has 3 elements.

In option C, there are exactly 3 y-coordinates, 5, 9, 15. The range is {5, 9, 15}. This set has 3 elements, and this is what I think they are looking for as the correct answer.

According to their logic, there is an inconsistency in their intended answer. If options B and D do not count because there are 4 y-coordinates, although 1 is repeated, so they count repeats, then option A should work because it has 3 points with 3 y-coordinates although all y-coordinates are the same number, 4.

If you need to choose one option, then my guess is that they meant for C to be correct because you only see 3 numbers for the y-coordinates. I still think that options B, C, and D are correct, and the problem is poorly worded.

Answer 5

In the end, B was correct because there were four different x values. As long as the x's are different, you can have the same y. There are three y values, and only one is used twice. I do agree that it was poorly worded.

Answer 6

Thanks for getting back with the correct answer.

Ok, now that I see it again, I see what I missed.
They are looking for two things in the answer:
1. the relation must be a function
2. the range must contain exactly 3 elements

Option A. All x's are different making it a function, but the range is only 4, one element.
Option B. All x's are different making it a function. The range contains exactly 3 elements.
Option C. x is 0 twice. It is not a function.
Option D. x is 3 twice. It is not a function.

The only option that is both a function and whose range has exactly 3 elements is option B. Therefore, option B is the correct answer.

It turns out the problem is not poorly worded. I misread the problem and thought they were asking for a relation with exactly 3 elements in the range,. That is why I thought there were several possible answers. Now that I see the wording of the problem includes function, I see what the problem means. Sorry for the confusion and my mistake.