The 2nd option does not represent a function.
A function is a relation in which no two ordered pairs have the same first component and different second components.
We need to ask ourselves, does every first element (or input) correspond with EXACTLY ONE second element (or output)?
In this case, the answer is no. The input value of 1 goes with two output values, -1 and -5. The same goes with the input value of 2, which also goes with two output values: -2 and -4.
It only takes one input value to associate with more than one output value to be invalid as a function.
I also did the Vertical Line Test to show why Option 2 is not a function. The Vertical Line Test 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.
However, the graph shows that the two vertical lines crossed the graphed twice (there are 2 points in each line). The graphed points failed the vertical line test. Therefore, Option 2 is NOT a function.
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