Question

which graph represents a function?

Explanation:

Step1: Recall the vertical line test

A graph represents a function if every \( x \)-value has at most one \( y \)-value. For discrete points, we check if any \( x \)-coordinate is repeated with different \( y \)-coordinates.

Step2: Analyze each graph

• First graph: Check \( x \)-coordinates. Some \( x \)-values have multiple \( y \)-values (e.g., \( x = 1 \) has multiple points), so not a function.
• Second graph: Check \( x \)-coordinates. Some \( x \)-values (e.g., \( x \) of the rightmost vertical line) have multiple \( y \)-values, so not a function.
• Third graph: Check \( x \)-coordinates. Each \( x \)-value (the \( x \)-coordinates of the points) has only one \( y \)-value. No repeated \( x \)-coordinates with different \( y \)-coordinates.
• Fourth graph: The \( x \)-coordinate (the same \( x \) for all points) has multiple \( y \)-values, so not a function.

Answer:

The third graph (the one in the middle-right among the four)