Domain, Range, and 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 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

Is the relation {(1,2), (2,3), (1,4)} a function?

Back

No, because the input '1' has two different outputs (2 and 4).

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase.

Front

What does it mean if a function is decreasing?

Back

A function is decreasing if, as the x-values increase, the y-values decrease.

Front

What is a vertical line test?

Back

A method to determine if a relation is a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is an example of a function?

Back

f(x) = 2x + 3 is a function because each x-value has one corresponding y-value.

Front

What is an example of a non-function?

Back

y^2 = x is not a function because each x-value can correspond to two y-values (positive and negative).

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input.