Functions

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 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 ordered pairs have the same first element (x-value) but different second elements (y-values).

Front

What is the vertical line test?

Back

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

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is a mapping in relation to functions?

Back

A mapping is a way to describe how each element of the domain is paired with an element of the range.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x gives a unique output.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, because the input 1 is associated with two different outputs.