Questions: Select all of the following graphs which represent y as a function of x.

Select all of the following graphs which represent y as a function of x.
Transcript text: Select all of the following graphs which represent $y$ as a function of $x$.
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Solution

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Solution Steps

Step 1: Recall the definition of a function

A graph represents \(y\) as a function of \(x\) if and only if every vertical line intersects the graph at most once. This is known as the vertical line test.

Step 2: Apply the vertical line test to each graph
  • Graph 1: Passes the vertical line test.
  • Graph 2: Passes the vertical line test.
  • Graph 3: Passes the vertical line test.
  • Graph 4: Passes the vertical line test.
  • Graph 5: Fails the vertical line test.
  • Graph 6: Fails the vertical line test.

Final Answer

Graphs 1, 2, 3, and 4 represent \(y\) as a function of \(x\).

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