Domain, Range, & Functions

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What is the domain of a function?

Back

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

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

How can you determine if a relation is a function using the vertical line test?

Back

If a vertical line intersects the graph of the relation at more than one point, then the relation is not a function.

Front

Given the relation {(1, 2), (2, 3), (3, 4)}, what is the domain?

Back

D = {1, 2, 3}.

Front

Given the relation {(1, 2), (1, 3), (2, 4)}, is this a function?

Back

No, because the input '1' corresponds to two different outputs (2 and 3).

Front

What is an example of a function?

Back

f(x) = x^2 is a function because each input x has exactly one output.

Front

What is a non-example of a function?

Back

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

Front

What is the domain of the function f(x) = 1/x?

Back

The domain is all real numbers except x = 0.

Front

What is the range of the function f(x) = x^2?

Back

The range is all real numbers greater than or equal to 0.