![]() For this $f$, the range is the set of non-negative real numbers while the codomain is the set of all real numbers. Solution: (a) The range for group of girls 10 6 4. We could combine the data provided with our own experiences and reason to approximate the domain and range of the function h f(c). The range formula determines the difference between the highest and the lowest values in a given set of numbers. Since $f(x)$ will always be non-negative, the number $-3$ is in the codomain of $f$, but it is not in the range, as there is no input of $x$ for which $f(x)=-3$. Learn the range math definition and see range math examples. It is possible there are objects in the codomain for which there are no inputs for which the function will output that object.įor example, we could define a function $f: \R \to \R$ as $f(x)=x^2$. ![]() ![]() All we know is that the range must be a subset of the codomain, so the range must be a subset (possibly the whole set) of the real numbers. But, without knowing what the function $f$ is, we cannot determine what its outputs are so we cannot what its range is. Learn the definition, formula and examples of the range of a function, the set of all possible outputs the function can produce. From this notation, we know that the set of all inputs (the domain) of $f$ isi the set of all real numbers and the set of all possible inputs (the codomain) is also the set of all real numbers. In the function machine metaphor, the range is the set of objects that actually come out of the machine when you feed it all the inputs.įor example, when we use the function notation $f: \R \to \R$, we mean that $f$ is a function from the real numbers to the real numbers. The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs.
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