Algebra II: Modeling and Functions
Functions are processes that take some input and produce some output, where every valid input produces only one specific output.
If inputs are on the horizontal -axis and outputs are on the vertical -axis on the graphs below, how many of them are functions?
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1 solution
Graph C includes the points ( 1 , 1 ) and ( 1 , 2 ) . This means an input of 1 has outputs of both 1 and 2 , so the graph does not represent a function. One way to think of this is the fact if you draw a vertical line through 1 , it passes through more than one point.
The other graphs pass this vertical line test . Both A and D have input values that aren't part of the graph, but we only need one specific output in the case of valid input.
Also note that the horizontal line portion of D doesn't affect its function status. It has, for example, the points ( 1 , 1 ) and ( 2 , 1 ) . The points 1 and 2 both give an output of 1. This is fine with functions; different inputs can give the same output. The disallowed scenario is for the same input to have multiple outputs.