A numerical relation R is a function if and only no vertical line in the plane intersects the graph of R in more than one point.a.Falseb.True

Break Down the Problem

1. Identify the definition of a function.
2. Understand the concept of the vertical line test.

Relevant Concepts

1. Definition of a Function: A relation $R$ is a function if, for every input (or x-value), there is exactly one output (or y-value).
2. Vertical Line Test: This is a visual way to determine whether a curve is a graph of a function or not. If a vertical line intersects the graph at more than one point, then the relation is not a function.

Analysis and Detail

1. If a vertical line intersects the graph in more than one point, it indicates that there are multiple outputs (y-values) for a single input (x-value), which contradicts the definition of a function.
2. Therefore, if no vertical line intersects the graph of the relation $R$ in more than one point, it confirms that $R$ is indeed a function.

Verify and Summarize

The statement given in the question follows the definition of a function and the vertical line test correctly. By ensuring that no vertical line intersects the graph at more than one point, we can conclude that the relation is a function.

Final Answer

b. True