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Domain and range
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The domain of a function is the set of possible inputs, and the range is the set of possible outputs.
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Domain of a function
SL Core 2.2
The domain of a function is the set of possible inputs it can be given.
The "natural" or "largest possible" domain of a function is all the values of x for which the expression f(x) is defined.
Range of a function
SL Core 2.2
The range of a function is the set of possible values it can output.
If the domain of the function is restricted, the range may need to be restricted as a consequence.
Notation for domain and range intervals
SL Core 2.2
The domain and range of functions are commonly intervals of real numbers.
For example, if f(x) is defined for 1<x≤5, we can write the domain
{x∈R∣1<x≤5}
(∈ means "in" or "element of", and R is all real numbers)
We can also use the equivalent interval notation
x∈]1,5]
where, by IB convention, an outward facing [ means that end is not inclusive (1<x) and an inward facing ] means that end is inclusive (x≤5).
Another common interval notation is
x∈(1,5]
where ( indicates a non-inclusive endpoint and ] indicates an inclusive endpoint. In this style, all brackets are inward facing.
These can also be visualized on a number line:
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