To apply the vertical line test to determine if the given relation (a half-circle) is a function, you can follow this reasoning:
A relation is a function if every vertical line drawn on the graph intersects the curve at most once.
For a half-circle, consider the following:
- A half-circle would typically look like a semicircle either opening upwards or downwards.
- If the half-circle is oriented upwards (like the upper half of a circle), then any vertical line will intersect the graph at exactly one point.
- If the half-circle is oriented downwards (like the lower half of a circle), again, any vertical line will intersect it at exactly one point.
In either case, a half-circle passes the vertical line test because it does not have any vertical lines that intersect the curve more than once.
Therefore, for a half-circle, the answer would be:
Yes, the given relation is a function.