2.1 Functions
Ideas in this lesson
- Recognize functions and identify inputs and outputs
- Translate rules and machine diagrams
- Evaluate numerical inputs and tables
- Evaluate symbolic inputs and distinguish operations
- Evaluate piecewise rules at boundaries
- Calculate and interpret net change
- Simplify difference quotients with restrictions
- Find polynomial domains and restricted ranges
- Find rational-function domains
- Find domains of even and odd roots
- Combine domain restrictions
- Connect verbal, formula, table, and graph representations
- Evaluate and interpret physical models
- Build contextual piecewise cost rules
- Create qualitative and data-based graphs
- Reason about unusual functions and model limitations
Recognize functions and identify inputs and outputs · Worked example
For a fixed sensor, \(T(t)\) records temperature 4 minutes after startup. Identify the independent and dependent quantities.
Answer: Independent: elapsed time; dependent: recorded temperature.
The input is elapsed time.
The rule returns one recorded temperature for that time.
Thus temperature depends on time in this model.
The rule returns one recorded temperature for that time.
Thus temperature depends on time in this model.