Overview
This lecture explains how to find the domain and range from a graph using interval notation, with examples covering open and closed endpoints and infinite intervals.
Key Definitions
- A relation is any set of ordered pairs.
- The domain is the set of all first components (x-values) in the ordered pairs.
- The range is the set of all second components (y-values) in the ordered pairs.
Example 1: Interval with Open and Closed Endpoints
- The domain includes all x-values from -3 (open) to 4 (closed), written as (-3, 4].
- The range includes all y-values from -2 (open) to 1 (closed), written as (-2, 1].
Example 2: Infinite Domain, Restricted Range
- The domain includes all real numbers, from -infinity to infinity, written as (-∞, ∞).
- The range begins at y = 2 (closed endpoint) and continues to infinity, written as [2, ∞).
Example 3: Infinite Domain and Range
- The domain includes all real numbers, written as (-∞, ∞).
- The range includes all real numbers, written as (-∞, ∞).
Interval Notation Principles
- Use round brackets ( ) for open endpoints (not included).
- Use square brackets [ ] for closed endpoints (included).
- Write intervals from lowest value to highest: left to right.
Key Terms & Definitions
- Domain — set of all possible x-values in a relation or function.
- Range — set of all possible y-values in a relation or function.
- Relation — any set of ordered pairs (x, y).
- Interval notation — a way to write subsets of the real number line using brackets for inclusion or exclusion.
Action Items / Next Steps
- Practice finding the domain and range for several graphs using interval notation.