Answer:
1st option (parabola) represents a function
Step-by-step explanation:
A relation is a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to.
To check whether a relation is a function, you can apply vertical line test. For an arbitrary x, draw vertical line and this line must intersect the graph of the relation at exactly one point.
Check all options:
1. Each vertical line intersects the graph of the relation at exactly one point - this is a function.
2. The graph shows vertical line x = 3. So, there are infinitely many points of intersection - this is not a function.
3. For all x > 0, vertical lines intersect the graph of the relation in two distinct points - this is not a function.
4. Vertical lines intersect circle at two points (except points where circle intersects x-axis) - this is not a function.
