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: if any vertical line drawn through the graph intersects the graph at more than one point, it is not a function.

Step2: Test each graph

• Top - left graph (circle): A vertical line (e.g., \(x = 0\)) will intersect the circle at two points. So it is not a function.
• Top - right graph (circle): A vertical line (e.g., \(x = 0\)) will intersect the circle at two points. So it is not a function.
• Bottom - left graph (curve): Any vertical line will intersect this curve at most once. So it passes the vertical line test.
• Bottom - right graph (curve): A vertical line (e.g., the line through the "loop") will intersect the curve at two points. So it is not a function.

Answer:

The Bottom - Left Graph