Functions vs Non Function

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is a non-function?

Back

A non-function is a relation where at least one input is related to more than one output.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

Example of a function: y = 2x + 3. Is this a function?

Back

Yes, this is a function because for every x-value, there is exactly one y-value.

Front

Example of a non-function: y^2 = x. Is this a function?

Back

No, this is not a function because for some x-values, there are two corresponding y-values.

Front

What does it mean for a table to represent a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value).

Front

If a graph passes the vertical line test, what can we conclude?

Back

If a graph passes the vertical line test, we can conclude that it is a function.

Front

What is an example of a non-function in a table?

Back

A table with the pairs (1, 2), (1, 3) is a non-function because the input 1 corresponds to two different outputs.

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, which can represent a function or a non-function.

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.