Is This Graph a Function? Exploring with the Vertical Line Test

Is the given graph a function?

To determine if the graph is a function, we will use the Vertical Line Test.

The Vertical Line Test states that a graph represents a function if and only if no vertical line intersects the graph at more than one point.

Let's apply this test to the given graph, where a horizontal line is drawn. This line represents the function the graph should be verified against.

• Step 1: Conceptualize vertical lines passing through different x-values across the domain of the graph.
• Step 2: Observe if any of these vertical lines intersect the graph at more than one point.

Upon inspection of the graph, we see that every vertical line intersects the graph at exactly one point.

This indicates that for every input (x-value), there is a unique output (y-value), fulfilling the criteria for the definition of a function.

Therefore, according to the Vertical Line Test, the given graph is indeed a function.

The correct choice is: Yes