Problem
1. Explain why R: x = 2y + sin(y) is a NOT function.
2. Graph relation R and use the vertical line test to verify it is NOT a function.
Solution
1. Explain why R: x = 2y + sin(y) is a NOT function.
Since it is not possible to isolate y in relation R, relation R is NOT a function..
2. Graph relation R and use the vertical line test to verify it is NOT a function.
The graph of relation R is shown below.
The vertical line test: If a vertical line can be drawn anywhere in the coordinate plane so that it intersects the graph of a relation at more than one location, then the relation is NOT a function.
In this example, a vertical line intersects the graph of the relation at more than one location for at least one value of x. As a result, the vertical line test indicates that the relation R (x = 2y + sin(y)) is NOT a function.
