Grade Math DCA 1 [23 Items] All Items 11-20 21 22 23 P Done ? Which representation shows y as a function of x? A.? X y -4 -8 0 3 1 2 -4 10 B.? X y -1 0 -1 5 -1 10 -1 15 C.? X y -2 -7 0 1 8 1 9 18
The Correct Answer and Explanation is:
The correct answer is: A
Explanation:
A function is a relation in which each input (x-value) has exactly one output (y-value). That means for every x, there must be only one corresponding y. Let’s analyze each option:
Option A:
| x | y |
|---|---|
| -4 | -8 |
| 0 | 3 |
| 1 | 2 |
| -4 | 10 |
Notice that the x-value -4 appears twice, once with y = -8 and again with y = 10. This means that one input leads to two different outputs, which violates the definition of a function.
So, A is NOT a function.
Option B:
| x | y |
|---|---|
| -1 | 0 |
| -1 | 5 |
| -1 | 10 |
| -1 | 15 |
Here, -1 is repeated as an x-value four times, each time with a different y-value (0, 5, 10, 15). Again, this means one input produces multiple outputs, so B is also NOT a function.
Option C:
A mapping diagram is shown. Let’s examine it:
- x = -2 → y = -7
- x = 0 → y = 1
- x = 8 → y = 1
- x = 9 → y = 18
Each x-value is paired with only one y-value. Even though both x = 0 and x = 8 lead to y = 1, that’s allowed — multiple x-values can point to the same y-value in a function. The key is that each x has only one arrow coming out.
Therefore, Option C does represent a function.
Final Answer: C
Because it is the only representation in which each input (x) corresponds to exactly one output (y), satisfying the definition of a function.
