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 does it mean for x-values to repeat in a relation?

Back

If x-values repeat in a relation, it means that the same input is associated with more than one output, which indicates that the relation is not a function.

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if no x-value is paired with more than one 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 a vertical line intersects the graph at more than one point, it is not a function.

Front

Which of the following is a function: {(1,2), (2,3), (3,4)} or {(1,2), (1,3)}?

Back

{(1,2), (2,3), (3,4)} is a function because each x-value is unique.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represents a point in a coordinate system.

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 definition of a relation?

Back

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

Front

How do you identify a function from a set of ordered pairs?

Back

To identify a function, check that no x-value appears more than once in the set of ordered pairs.

Front

What is the significance of the x-value in a function?

Back

The x-value is the input of the function, which determines the corresponding y-value (output).