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 a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is paired with more than one y-value.

Front

What does it mean if a relation is not a function?

Back

It means that at least one x-value is paired with multiple y-values.

Front

Example of a function: (2,3), (3,4), (4,5)

Back

This is a function because each x-value (2, 3, 4) has a unique y-value (3, 4, 5).

Front

Example of a relation that is not a function: (1,2), (1,3), (2,4)

Back

This is not a function because the x-value 1 is paired with two different y-values (2 and 3).

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

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value has only one y-value.

Front

What is an example of a function with repeated y-values?

Back

The function f(x) = x^2 has the same y-value for both x = 2 and x = -2 (both give y = 4).

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its output.