Question

use the vertical line test to determine which of the following graphs are graphs of functions. (select all that apply)

Explanation:

Step1: Recall the vertical line test

A graph is a function if and only if every vertical line intersects the graph at most once.

Step2: Analyze the first graph (left - top)

For any vertical line \(x = a\), it intersects the graph at most once.

Step3: Analyze the second graph (right - top)

There exists a vertical line (for example, near the origin) that intersects the graph more than once.

Step4: Analyze the third graph (left - bottom)

For any vertical line \(x = a
eq0\), it intersects the graph at most once. When \(x = 0\), the vertical line \(x = 0\) does not intersect the graph (since the graph has a break at \(x = 0\)).

Step5: Analyze the fourth graph (right - bottom)

For any vertical line \(x = a\), it intersects the graph at most once.

Answer:

The first (left - top), third (left - bottom) and fourth (right - bottom) graphs are graphs of functions.