Questions: Which of the graphs below are graphs of functions and which are not? If a graph is not a graph of a function, explain why not.

Which of the graphs below are graphs of functions and which are not? If a graph is not a graph of a function, explain why not.
Transcript text: Which of the graphs below are graphs of functions and which are not? If a graph is not a graph of a function, explain why not.
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Solution

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Solution Steps

Step 1: Identify the Vertical Line Test

To determine if a graph represents a function, we use the vertical line test. A graph represents a function if and only if no vertical line intersects the graph at more than one point.

Step 2: Analyze Graph (a)

Graph (a) shows a diagonal line. Applying the vertical line test, any vertical line will intersect the graph at exactly one point. Therefore, graph (a) represents a function.

Step 3: Analyze Graph (b)

Graph (b) shows multiple points aligned vertically. Applying the vertical line test, a vertical line will intersect the graph at multiple points. Therefore, graph (b) does not represent a function.

Step 4: Analyze Graph (c)

Graph (c) shows a horizontal line. Applying the vertical line test, any vertical line will intersect the graph at exactly one point. Therefore, graph (c) represents a function.

Final Answer

  • Graph (a) is a graph of a function.
  • Graph (b) is not a graph of a function because a vertical line intersects it at multiple points.
  • Graph (c) is a graph of a function.
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