Functions, Domain & Range

Front

What is a function?

Back

A function is a relation where each input has exactly one output.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

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

Back

A relation is a function if it passes the vertical line test, meaning no vertical line intersects the graph at more than one point.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if any vertical line crosses the graph more than once, it is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one; if any horizontal line crosses the graph more than once, it is not one-to-one.

Front

How do you find the domain from a graph?

Back

The domain can be found by identifying all the x-values that the graph covers.

Front

How do you find the range from a graph?

Back

The range can be found by identifying all the y-values that the graph covers.

Front

What is an example of a function?

Back

f(x) = 2x + 3 is a function because for every x, there is exactly one y.

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 has two different outputs.