This graph is a function.
Domain: [-3, 4]
Range: [0, 4]
Step-by-step explanation:
The given graph represents a function because every input value corresponds to exactly one output value.
The Vertical Line Test (VLT) allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.
To use the VLT, imagine dragging a ruler held vertically across the graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value. If you do this for the given graph, every vertical line intersects the graph in at most one point. Hence, this graph is the graph of a function.
Attached is a screenshot where it shows that each vertical line drawn crosses the graph at most once. Since the graph passed the VLT, it means that the graph is a function.
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