The domain of a function is the set of possible inputs, and the range is the set of possible outputs.
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.
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.
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
(∈ means "in" or "element of", and R is all real numbers)
We can also use the equivalent interval notation
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
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:
Nice work completing Domain and range, here's a quick recap of what we covered:
Exercises checked off
The domain of a function is the set of possible inputs, and the range is the set of possible outputs.
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.
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.
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
(∈ means "in" or "element of", and R is all real numbers)
We can also use the equivalent interval notation
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
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:
Nice work completing Domain and range, here's a quick recap of what we covered:
Exercises checked off