Which table shows a function whose range has exactly three elements?
x |f(x)
1 | 4
2 | 4
3 | 4
///////
x |f(x)
3 | 8
4 | 6
5 | 12
6 | 8
///////
x |f(x)
0 | 5
2 | 9
0 | 15
///////
x |f(x)
1 | 4
3 | 2
5 | 1
3 | 4
Is the answer D?
Not D, because f(3) has two different values. So, f is not a function.
Is it C? All the f(x) values are different.
To determine which table shows a function whose range has exactly three elements, we need to find the table where the range contains only three different values.
For Option D:
x | f(x)
1 | 4
3 | 2
5 | 1
3 | 4
We have four values in the range: 4, 2, 1, and 4. Therefore, Option D does not have a range with exactly three elements.
Let's evaluate the other options:
For Option A:
x | f(x)
1 | 4
2 | 4
3 | 4
In this case, we have only one value, 4, in the range. Therefore, Option A does not have a range with exactly three elements.
For Option B:
x | f(x)
3 | 8
4 | 6
5 | 12
6 | 8
In this case, we have three unique values in the range: 8, 6, and 12. Therefore, Option B satisfies the condition of having a range with exactly three elements.
For Option C:
x | f(x)
0 | 5
2 | 9
0 | 15
In this case, we have three unique values in the range: 5, 9, and 15. Therefore, Option C also satisfies the condition of having a range with exactly three elements.
Based on the analysis, the correct answer is **Option B**, where the table shows a function whose range has exactly three elements.