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

///////

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

Is the answer C? I was also thinking A since the f(x) values are 4, but the regular x values are different, thereby not contradicting it to be a function.

I think option A is the best one, but the assessment says that B is correct. However, the lesson states that you can as long as each element(x) is different, you can have the same y value in the second column.

In a function, the same x value cannot have 2 or more different y values

This happens in C and D, so those two are NOT functions

That leaves A and B, but A led me to the objection I first stated.

To determine which table represents a function whose range has exactly three elements, we need to check if the given tables meet the criteria for a function.

A function is a relation in which each input has a unique output. This means that for each distinct value of x, there should be only one corresponding value of f(x).

Let's analyze each table:

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

In this table, for every value of x, the corresponding f(x) value is 4. The range of this table only has one element, which is 4. So, this table does not have a range with exactly three elements.

Table 2:
x | f(x)
3 | 8
4 | 6
5 | 12
6 | 8

In this table, each value of x has a unique corresponding f(x) value, and the range of this table is {8, 6, 12}, which has exactly three elements. So, this table represents a function whose range has exactly three elements.

Table 3:
x | f(x)
0 | 5
2 | 9
0 | 15

In this table, we observe that there are duplicate x values (0) with different corresponding f(x) values (5 and 15). This violates the definition of a function since each x should have only one corresponding f(x) value. Therefore, this table does not represent a function.

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

In this table, we have a duplication of an x value (3) with different corresponding f(x) values (2 and 4). Once again, this violates the definition of a function. Hence, this table does not represent a function.

Therefore, the correct answer is Table 2:

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

The answer is 54 to my own understanding

poor wording, you must have meant

three "different" values.