Identifying functions

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 vertical line test?

Back

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

Front

How can you tell if a mapping is a function?

Back

A mapping is a function if each input value corresponds to exactly one output value.

Front

What does it mean if x-values repeat in a mapping?

Back

If x-values repeat in a mapping, it means the mapping is not a function because one input is associated with multiple outputs.

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, which can include functions but does not have to.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has one corresponding y-value.

Front

What is an example of a non-function?

Back

An example of a non-function is y^2 = x, where one x-value can correspond to multiple y-values.

Front

What does it mean for a graph to be a function?

Back

A graph is a function if every vertical line drawn through the graph intersects it at most once.

Front

What is the significance of the output in a function?

Back

The output in a function is the result of applying the function to an input, and it must be unique for each input.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.