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? 

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  • 1 month ago
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    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*.

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  • 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).

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  • 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.

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  • 1 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.

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