Anatomy of a Function
A function is a special type of structure called a relation.
As a relation, a function is a package containing three sets.
- One set is called the domain.
- One set is called the codomain.
- Finally, there is a third set of pairings. Each pairing associates a member of the domain with a member of the codomain. This third set does not seem to have an official title.
While a relation is just two sets of items and some pairings between the two sets, functions satisfy one rule:
- Functions are those relations where each domain item is paired with exactly one codomain item.
OR
This simple rule makes a world of difference. But, we can do a little better for this course.
This course (and Calculus) is a study of measurements and how they compare to each other. Since measurements consist of scalars (numbers) and units, this means this course (and Calculus) is a study of the real numbers. Therefore, the domains and ranges of our functions will be subsets of the real numbers. We say that our functions map real numbers to real numbers.
\(f : \mathbb {R} \mapsto \mathbb {R}\)
With the addition of this one rule and the restriction of our domains and codomains to be sets of real numbers, we are ready to begin our journey towards Calculus.
Learning Outcomes
In this section, students will
- use function notation.
- evaluate functions.
- solve equations involving functions.
- analyze functions.
- focus on numeric functions.
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more examples can be found by following this link
More Examples of Functions