Appendix C Theory
1.1 What is a function?
Theorem 1.1.36 Vertical line test
1.2 Linear and quadratic functions
Theorem 1.2.18 Properties of linear functions
Procedure 1.2.21 Equations of lines
Theorem 1.2.24 Zero product
Theorem 1.2.27 Quadratic formula
Procedure 1.2.29 Solving quadratic equations
Theorem 1.2.31 Quadratic factoring identities
Theorem 1.2.33 Properties of quadratic functions
1.3 Modeling with Linear and Quadratic Functions
Theorem 1.3.4 Linear function equivalence
Theorem 1.3.16 Height of falling object
1.4 Algebraic functions
Theorem 1.4.5 Power identities
Corollary 1.4.8 Radical identities
1.5 Algebraic functions: continued
Theorem 1.5.10 Roots of polynomials
Procedure 1.5.11 Polynomial long division
Theorem 1.5.15 Integer root theorem
Procedure 1.5.18 Factoring polynomials and finding roots
Theorem 1.5.21 Factoring tools
Procedure 1.5.22 Solving polynomial equations
Corollary 1.5.26 Polynomial equality
Theorem 1.5.27 Quotients of functions
Corollary 1.5.28 Domain and zeros of rational functions
1.6 Transformations and symmetry
Theorem 1.6.14 Function transformations
Theorem 1.6.33 Vertex form
1.8 Solving inequalities
Theorem 1.8.1 Elementary inequality rules
Theorem 1.8.8 Sign of a product
Theorem 1.8.11 Constancy of sign: algebraic functions
Procedure 1.8.12 Sign diagram
Theorem 1.8.15 Inequalities and squares
1.10 Piecewise-defined functions and absolute value
Theorem 1.10.14 Absolute value function is algebraic
Theorem 1.10.16 Properties of absolute value
Procedure 1.10.21 Graphing \(f(x)=\abs{g(x)}\)
1.11 Introduction to limits
Theorem 1.11.15 One-sided limits test
1.12 Limit rules
Theorem 1.12.1 Constant and identity function formulas
Theorem 1.12.2 Limit rules
Theorem 1.12.6 Polynomial and rational function evaluation
Theorem 1.12.11 Absolute value evaluation
1.14 Limits: formal definition
Procedure 1.14.10 Epsilon-delta proof for limits
Theorem 1.14.15 Triangle inequality
1.15 Continuity
Theorem 1.15.10 Continuous functions
Theorem 1.15.11 Continuity rules
Theorem 1.15.12 Continuity composition rule
Theorem 1.15.13 Algebraic functions are continuous
Theorem 1.15.14 Algebraic function evaluation
Theorem 1.15.18 Intermediate value theorem (IVT)
Theorem 1.15.23 Constancy of sign: continuous functions
1.16 Limits at infinity
Theorem 1.16.7 Limit at infinity formulas
1.17 Infinite limits
Theorem 1.17.5 Power functions and their reciprocals
Theorem 1.17.6 Infinite limit formulas
Theorem 1.17.9 Limit at infinity: rational functions
