Unit 1
Polynomial and Rational Functions
Rates of change, then polynomial and rational functions: zeros, end behavior, asymptotes, holes, transformations and building a model.
Topics
- 1.1Change in Tandem
- 1.2Rates of Change
- 1.3Rates of Change in Linear and Quadratic Functions
- 1.4Polynomial Functions and Rates of Change
- 1.5Polynomial Functions and Complex Zeros
- 1.6Polynomial Functions and End Behavior
- 1.7Rational Functions and End Behavior
- 1.8Rational Functions and Zeros
- 1.9Rational Functions and Vertical Asymptotes
- 1.10Rational Functions and Holes
- 1.11Equivalent Representations of Polynomial and Rational Expressions
- 1.12Transformations of Functions
- 1.13Function Model Selection and Assumption Articulation
- 1.14Function Model Construction and Application
Unit check
14 questions drawn from every lesson in Unit 1. Each wrong answer links back to where the idea is taught.
Labs for this unit
- Topics 1.12, 2.3, 2.4, 2.7, 2.11, 2.12, 3.5 and 3.6 Function Grapher Move a, b, c and d in g(x) = a f(b(x + c)) + d and watch a polynomial, rational, exponential, logarithmic or sine graph transform.
- Topics 1.14, 2.5, 2.6 and 2.14 Model Builder Fit a linear, quadratic, cubic, quartic, exponential or logarithmic regression to a small data set, then read the residual plot to decide whether the model is appropriate.