Questions: Which of these relations is a function?

Transcript text: Which of these relations is a function?

Solution

Solution Steps

Step 1: Recall the definition of a function

A function is a relation where each input (x-value) has exactly one output (y-value). This means any vertical line drawn on the graph of a function will intersect the graph at most once. This is known as the vertical line test.

Step 2: Apply the vertical line test to each graph

Top Left: Any vertical line will only cross the graph once. This is a function.
Top Right: Any vertical line will only cross the graph once. This is a function.
Bottom Left: A vertical line can cross the graph twice. This is not a function.
Bottom Right: Any vertical line will only cross the graph once. This is a function.

Final Answer:

The top left, top right, and bottom right graphs represent functions.

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