Functions

Front

What is a function?

Back

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

Front

How can you determine 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.

Front

What is a mapping in the context of functions?

Back

A mapping shows how each element of a set (domain) is paired with an element of another set (range).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function by checking if a vertical line crosses the curve more than once.

Front

What does it mean if a relation is 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

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Give an example of a function using a table.

Back

Example: x | y ----|---- 1 | 2 2 | 3 3 | 4 (This is a function because each x-value has one y-value.)

Front

Give an example of a relation that is not a function using a mapping.

Back

Example: x | y ----|---- 1 | 2 1 | 3 (This is not a function because the x-value 1 has two y-values.)