Answer:
Option II: I and III are not functions
Step-by-step explanation:
A function is a relation in which no two ordered pairs have the same input (or x-values) and different outputs (y-values). In other words, a function can only take on one output for each input.
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 graphs, every vertical line intersects the graph in at most one point represents a function. It only takes one input value to associate with more than one output value to be invalid as a function.
As you can see in the edited screenshot, the vertical lines drawn on graph 1 crosses the graph more than once, that is why it is not a function. The 2nd graph is a function, because each vertical line crosses the graph only once.
The 3rd graph is definitely not a function because the vertical line crosses the graph more than once.
Therefore, the correct answer is option II: I and III
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