which of the following is a function?

Explanation:

Step1: Recall the vertical line test

A relation is a function if for every (x -) value there is exactly one (y -) value. The vertical line test states that if a vertical line intersects the graph of a relation at more than one point, the relation is not a function.

Step2: Analyze the first graph (points)

For the set of points, assume no two points have the same (x -) coordinate. Each (x) has a unique (y).

Step3: Analyze the second graph (V - shaped with multiple (y) for some (x))

A vertical line (e.g., (x=- 4)) would intersect this graph at more than one point. So, it fails the vertical line test.

Step4: Analyze the third graph (curve with multiple (y) for some (x))

A vertical line (e.g., (x = 2)) would intersect this graph at more than one point. So, it fails the vertical line test.

Step5: Analyze the fourth graph (increasing curve, but check vertical line test)

Although it is increasing, if we consider the nature of the graph (assuming it's a non - function based on the general shape description, but more accurately, if we assume it's a parabola - like opening in a non - function way). But the first graph (points) passes the vertical line test as each (x) has a unique (y).

Answer:

The first graph (the set of points) is a function.