Function or Not a 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 the definition of an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, typically written as (x, y).

Front

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

Back

A relation is a function if no two different ordered pairs have the same first element (input).

Front

Which of the following is not a function: {(1, 2), (1, 3), (2, 4)}?

Back

It is not a function because the input '1' is associated with two different outputs (2 and 3).

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

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 any vertical line crosses the curve more than once.

Front

What is a domain in a function?

Back

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

Front

What is a range in a function?

Back

The range is the set of all possible output values (y-values) for a 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.

Front

What is an example of a function?

Back

An example of a function is f(x) = x + 2, where each input x has a unique output.