2.16 Functions, mappings, domain and range
A mapping transforms one set of numbers into another set.
A mapping is a function if every input leads to a distinct output. Functions can be one-to-one or many-to-one mappings. One-to-many mappings are not functions.
Domain and range
The domain of a mapping is the set of all possible inputs. Graphically, the domain is the set of possible \(x\) values.
The range of a mapping is the set of all possible outputs. Graphically, the range is the set of possible \(y\) values.
Notation
\(x∈ℝ\) means "\(x\) is in the set of all real numbers"
A mapping is a function if every input leads to a distinct output. Functions can be one-to-one or many-to-one mappings. One-to-many mappings are not functions.
A one-to-one mapping, therefore a function
A many-to-one mapping, therefore a function
A one-to-many mapping, therefore not a function
A many-to-many mapping, therefore not a function
Domain and range
The domain of a mapping is the set of all possible inputs. Graphically, the domain is the set of possible \(x\) values.
The range of a mapping is the set of all possible outputs. Graphically, the range is the set of possible \(y\) values.
Notation
\(x∈ℝ\) means "\(x\) is in the set of all real numbers"
Important
One-to-one and many-to-one mappings are functions.
One-to-many mappings are not functions.
The domain of a mapping is the set of all possible inputs. Graphically, the domain is the set of possible \(x\) values.
The range of a mapping is the set of all possible outputs. Graphically, the range is the set of possible \(y\) values.
\(x∈ℝ\) means "\(x\) is in the set of all real numbers"
One-to-many mappings are not functions.
The domain of a mapping is the set of all possible inputs. Graphically, the domain is the set of possible \(x\) values.
The range of a mapping is the set of all possible outputs. Graphically, the range is the set of possible \(y\) values.
\(x∈ℝ\) means "\(x\) is in the set of all real numbers"
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