Question

What are the rules to determine if a graph, table, map diagram, or set of ordered pairs is a function? What’s the exception to the rule?

Answer 1

Answer:

Rule : Vertical line test, unique output for each input, mapping should one-one and onto, each x-value has unique y-value.

Exception : Inverse trigonometric functions

Step-by-step explanation:

A relation is a function if there exist a unique output for each input value.

We use vertical line test to check whether the graph intersect a vertical line at most once or not. If it intersect the graph more than once than it is not a function.

In table, first we identify the input and output variable, then we check there exist a unique output for each input value.

In map diagram, we check each element in the domain must be matched with exactly one element in the range, i.e., one-one and onto, then it is called function.

Set of ordered pairs, we check that each x-value has unique y-value.

Exception to the rule : Inverse trigonometric functions are not real valued functions, so these are the exceptions.

For example : $sin^{-1}x, cos^{-1}x\text{ etc}$.