To determine whether the given relation represents a function, we need to check whether each input (independent variable [tex]\(x\)[/tex]) has exactly one output (dependent variable [tex]\(y\)[/tex]).
We are given the following points:
[tex]\[
\left(\frac{3}{4}, -2\right),\ (15, 2),\ (-2, -7),\ \left(3, -\frac{1}{2}\right),\ (6, 6)
\][/tex]
### Step-by-Step Solution:
1. List the x-values (independent variables) from each ordered pair:
[tex]\[
\frac{3}{4},\ 15,\ -2,\ 3,\ 6
\][/tex]
2. Check for repeating x-values:
- The x-values are [tex]\(\frac{3}{4}\)[/tex], [tex]\(15\)[/tex], [tex]\(-2\)[/tex], [tex]\(3\)[/tex], and [tex]\(6\)[/tex].
- There are no duplicates among these x-values.
3. Determine if the relation is a function:
- In a function, each unique input (x-value) corresponds to exactly one output (y-value).
- Since all x-values are unique and there are no repeated x-values, each input [tex]\(x\)[/tex] has exactly one output [tex]\(y\)[/tex].
### Conclusion:
- Since each input has exactly one output, the relation does represent a function.
Therefore, the correct answer is:
Yes, because for each input there is exactly one output
