Anatomy of a Function

Functions are special relations. While a relation is just two sets of items and some pairings between the two sets, functions satisfy one rule:

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, which means it 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.

$$\text { f : } \mathbb {R} \mapsto \mathbb {R}$$

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.