## Trending News

# 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?

### 4 Answers

- PuzzlingLv 71 month agoFavorite Answer
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*.

- Login to reply the answers

- no sea naboLv 61 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.PersonaLv 51 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).

- Login to reply the answers

- 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.

- Login to reply the answers

- Iggy RockoLv 71 month ago
The range is the set of all output values of a function. It's common to call an input, x, and an output, y, but not mandatory.

- Login to reply the answers