Final answer:
The relation is a function if it passes the Vertical Line Test, which means every x-value has a unique y-value, which is true for any straight line, horizontal or otherwise.
Step-by-step explanation:
To determine whether the relation is a function, we look at whether each input has exactly one output. Vertical Line Test, which states that if a vertical line intersects the graph of the relation at more than one point, then the relation is not a function. Now, let's consider the options:
- Option a) It is a straight line with negative slope. - A straight line, regardless of the slope (negative or positive), represents a function because it passes the vertical line test.
- Option b) It is a straight line with positive slope. - Similar to option a), this also represents a function due to passing the vertical line test.
- Option c) It is a horizontal line at some negative value. - A horizontal line also passes the vertical line test, thus it is a function.
- Option d) It is a horizontal line at some positive value. - This, too, passes the vertical line test, confirming it is a function.
The correct answer, therefore, is c) Yes, the function passes the vertical line test.