Function/NOT a Function

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is the definition of 'not a function'?

Back

A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

Front

How can you tell if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What does it mean if an x-value is repeated in a set of ordered pairs?

Back

If an x-value is repeated in a set of ordered pairs, it may indicate that the relation is not a function if the corresponding y-values are different.

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

Given the set {(2,3), (2,4), (3,5)}, is this a function?

Back

No, because the x-value 2 is associated with two different y-values (3 and 4).

Front

What is an example of a function?

Back

An example of a function is the relation {(1,2), (2,3), (3,4)}, where each x-value has a unique y-value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1,2), (1,3), (2,4)}, where the x-value 1 has two different y-values.

Front

If a table shows x-values 1, 2, 3, and 4 with corresponding y-values 5, 6, 7, and 8, is it a function?

Back

Yes, because each x-value has a unique y-value.

Front

What happens if a relation has two pairs with the same x-value but different y-values?

Back

The relation is not a function because one input (x-value) corresponds to multiple outputs (y-values).