Real-Valued

Real-Valued functions are functions whose values are real numbers, i.e. the range is a subset of the real numbers.

The functions in Calculus relate measurements, but to focus on the concepts and characteristics and properties, we often leave the units to the applied situations and focus our attention on numeric functions.

For our numeric functions, both the domain and range are subsets of the real numbers.

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

Therefore, this section lays the foundation for how we think about and talk about subsets of the real numbers.

Learning Outcomes

In this section, students will

• use interval notation to describe subsets of real numbers.
• investigate open sets.
• investigate examples of real-valued functions.