# Range of Functions?

What is the range of a function? I need an easy definition. Is the range of a function the y-coordinate of the point (x, y)? Fir example, (x, y) = (domain, range). Right?

Relevance
• 1 month ago

Pretty simply:

The domain is the set of all possible *input* values. In other words, it's all possible values of *x*.

The range is the set of all possible *output* values. In other words, it's all possible values of *y*.

• 1 month ago

When "range" is used to mean "codomain", the image of a function f is already implicitly defined. It is (by definition of image) the (maybe trivial) subset of the "range" which equals {y | there exists an x in the domain of f such that y = f(x)}.

When "range" is used to mean "image", the range of a function f is by definition {y | there exists an x in the domain of f such that y = f(x)}. In this case, the codomain of f must not be specified, because any codomain which contains this image as a (maybe trivial) subset will work.

In both cases, image f ⊆ range f ⊆ codomain f, with at least one of the containments being equality.

• Mr.Persona
Lv 5
1 month agoReport

Definitely agree that it's important to know about codomain. I.e. a function is a source set X, a destination set Y, and then the rule mapping between the two. Range should be specifically reserved to represent f(X).

• 1 month ago

The range of a function is every Y-value that can exist. AKA if you plug in a Y-value, you will get an X-value

For example, the range for sin(x) is -1 <= x <= 1

And I have not seen (x,y) used to denote domain and range; in my experiences, it is simply a point.