Questions: Which graph represents a function?

Which graph represents a function?
Transcript text: Which graph represents a function?
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Solution

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Solution Steps

Step 1: Define a function

A function is a relation where each input has only one output. Graphically, this means that any vertical line drawn through the graph will intersect the graph at most once. This is called the vertical line test.

Step 2: Apply the vertical line test

Consider a vertical line drawn at \(x = -1\).

  • Graph 1: The line intersects at two points.
  • Graph 2: The line intersects at two points.
  • Graph 3: The line intersects at one point.
  • Graph 4: The line intersects at one point.

Graphs 1 and 2 fail the vertical line test, therefore they are not functions.

Consider a vertical line drawn at any other x-coordinate. Graph 3 and Graph 4 pass the vertical line test.

Final Answer

The third and fourth graphs represent functions.

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