Functions, Domain and Range

Front

What is a function?

Back

A relation that maps every domain value to exactly one range value.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

The set of all possible output values (y-values) for the function.

Front

What is a mapping diagram?

Back

A visual representation that shows how each element of the domain is paired with an element in the range.

Front

What is the vertical line test?

Back

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

For the function: f(x) = 2x + 3, what is f(4)?

Back

11

Front

For the function: f(x) = x^2, what is the range?

Back

The range is all non-negative real numbers (y ≥ 0).

Front

What does it mean for a function to be one-to-one?

Back

Each element of the range is paired with exactly one element of the domain.

Front

What is an example of a function?

Back

f(x) = 3x - 5 is a function because each x-value has a unique y-value.

Front

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

Back

The relation {(1, 2), (1, 3)} is not a function because the input 1 maps to two different outputs.