Question

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Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). We can use the vertical line test to determine if a graph represents a function. The vertical line test states that if any vertical line drawn through the graph intersects the graph at more than one point, then the graph does not represent a function.

Step2: Apply the vertical line test to each graph

• Top - Left Graph (Circle): If we draw a vertical line through the circle, it will intersect the circle at two points. So, this graph does not represent a function.
• Top - Right Graph (Arrow - shaped): If we draw a vertical line through the "corner" area or other parts of this graph, it will intersect the graph at more than one point. So, this graph does not represent a function.
• Bottom - Left Graph (Piece - wise linear): For any vertical line we draw, it will intersect this graph at most one point. So, this graph passes the vertical line test and represents a function.
• Bottom - Right Graph (S - shaped curve): If we draw a vertical line through the curve, it will intersect the curve at two points. So, this graph does not represent a function.

Answer:

The Bottom - Left Graph (the graph in the bottom - left quadrant of the four - graph set)