use the vertical line test to select all graphs showing relations that are functions.

Explanation:

Step1: Recall vertical - line test

The vertical - line test states that a relation is a function if any vertical line drawn on the graph intersects the graph at most once.

Step2: Analyze first graph

For the first graph (upper - left), a vertical line can be drawn that intersects the graph at two points (near the y - axis where the graph has two branches). So, it is not a function.

Step3: Analyze second graph

For the second graph (upper - right), any vertical line drawn will intersect the graph at most once. So, it is a function.

Step4: Analyze third graph

For the third graph (lower - left), any vertical line drawn will intersect the graph at most once. So, it is a function.

Step5: Analyze fourth graph

For the fourth graph (lower - right), a vertical line through the break in the graph (at (x = 0)) will intersect the graph at two points (the two horizontal segments). So, it is not a function.

Answer:

The second and third graphs are functions.