How do you determine if (-1, 4), (2, 8), (-1, 5) is a function?

1 Answer
Dec 8, 2014

To be a function, only one output is a assigned to a given input. To determine if a relation (the ordered pairs) is a function, you can analyze the relation to see if there is only one output assigned to a given input or see if it passes the vertical line test.

In analyzing the the relation, the output is the dependent variable (y) and input is the independent variable (x). Of the ordered pairs: (-1,4), (2,8), (-1,5), the input -1 has been assigned to 5 and 4. It was repeated so therefore the relation is not a function. Basically to be a function, no input can be repeated.

To use the vertical line test, you want to graph the order pairs (coordinates) on the coordinate plane. When you draw vertical lines on the plane, if the line touches the graphed points more than once... the relation is not a function. That is what happens in this relation, if you draw a vertical line where x = -1, you see the line touches two coordinates (-1, 4) and (-1, 5). This proves that the relation is not a function.

In conclusion, (-1,4), (2,8), and (-1,5) is not a function.