Appendix D Examples
1.1 What is a function?
Example 1.1.2 Set membership
Example 1.1.5 Squaring function
Example 1.1.7 Square roots: a non-example
Example 1.1.13 Subsets of integers
Example 1.1.18 Union of intervals
Example 1.1.21 Implied domain: reciprocal function
Example 1.1.24 Range: squaring function
Example 1.1.25 Range: principal square-root function
Example 1.1.30 Graph: radical function
Example 1.1.32 Graph: rational function
Example 1.1.39 Vertical line test: radical function
Example 1.1.41 Relations and functions
1.2 Linear and quadratic functions
Example 1.2.3 Linear functions
Example 1.2.11 Desmos: family of linear functions
Example 1.2.13 Desmos: family of quadratic functions
Example 1.2.16 Linear function properties
Example 1.2.22 Equations of lines
Example 1.2.30 Quadratic equations
Example 1.2.32 Quadratic function properties
Example 1.2.35 Vertex form
1.3 Modeling with Linear and Quadratic Functions
Example 1.3.5 Average rate of change: linear functions
Example 1.3.8 Dolbear’s law
Example 1.3.12 Dolbear’s law: continued
Example 1.3.14 Modeling Glacier Areas
Example 1.3.17 Water ballon
Example 1.3.21 Radio production: cost function
Example 1.3.24 Radio production: revenue
Example 1.3.25 Radio production: cost and revenue
Example 1.3.27 Radio production: break-even point and fixed cost
1.4 Algebraic functions
Example 1.4.3 Power functions: implied domain
Example 1.4.4 Evaluating power functions
Example 1.4.17 Polynomials
Example 1.4.21 Rational function: like denominators
Example 1.4.22 Rational function: clear denominators
Example 1.4.27 Identifying algebraic function types
1.5 Algebraic functions: continued
Example 1.5.4 Power function: range
Example 1.5.7 Modeling with power functions
Example 1.5.12 Polynomial long division
Example 1.5.14 Polynomial root check
Example 1.5.16 Integer roots
Example 1.5.17 Polynomial roots
Example 1.5.19 Roots of a quartic
Example 1.5.23 Solving a polynomial equation
Example 1.5.29 Rational functions: domain and zeros
1.6 Transformations and symmetry
Example 1.6.1 Desmos: function transformations
Example 1.6.3 Vertical shift
Example 1.6.5 Horizontal shift
Example 1.6.7 Vertical scaling
Example 1.6.9 Horizontal scaling
Example 1.6.12 Vertical and horizontal reflection
Example 1.6.16 Transformations
Example 1.6.27 Even/odd power functions
Example 1.6.30 Even/odd/neither
1.7 Function composition
Example 1.7.7 Composition: evaluation and formulas
Example 1.7.8 Composition: order matters
Example 1.7.10 Expressing functions as compositions
Example 1.7.11 Composition: using tables
Example 1.7.12 Composition: using graphs
Example 1.7.13 Composition: implied domain
Example 1.7.14 Composition: implied domain
1.8 Solving inequalities
Example 1.8.4 Solving elementary inequalities
Example 1.8.13 Sign diagram: rational function
Example 1.8.14 Solving \(x^2> a\)
Example 1.8.16 Sign diagram: quartic
1.9 Domains of algebraic functions
Example 1.9.1 Domain of radical function
Example 1.9.2 Radical composed with quadratic
1.10 Piecewise-defined functions and absolute value
Example 1.10.12 Absolute value (piecewise)
Example 1.10.17 Absolute value algebra
Example 1.10.22 Transformed absolute value function
Example 1.10.24 Absolute value of quadratic
1.11 Introduction to limits
Example 1.11.1 Function behavior
Example 1.11.5 Limit description of graph
Example 1.11.6 Limit as compared to value
Example 1.11.10 Limits: using table of values
Example 1.11.13 Visualizing one-sided limits
1.12 Limit rules
Example 1.12.5 Using limit rules
Example 1.12.7 Polynomial and rational function evaluation
Example 1.12.9 Using limit rules
1.13 Limits: algebraic technique
Example 1.13.1 Quotient rule does not apply
Example 1.13.2 Algebraic limit technique: factoring
Example 1.13.3 Algebraic limit technique: clear denominator
Example 1.13.4 Algebraic limit technique: radicals
1.14 Limits: formal definition
Example 1.14.4 Epsilon-delta: linear function
Example 1.14.8 Visualizing epsilon-delta definition
Example 1.14.13 Epsilon-delta: radical function
Example 1.14.16 Proof of the sum rule for limits
1.15 Continuity
Example 1.15.5 Continuity at endpoint
Example 1.15.7 Continuity: graphical
Example 1.15.9 Continuous everywhere
Example 1.15.15 Algebraic function evaluation
Example 1.15.16 Continuity: piecewise
Example 1.15.20 Roots of polynomials
Example 1.15.21 IVT for an algebraic function
1.16 Limits at infinity
Example 1.16.9 Limit at infinity: reciprocal powers
Example 1.16.10 Limit at infinity: rational function
Example 1.16.11 Limit at infinity: radical function
1.17 Infinite limits
Example 1.17.7 Infinite limit
Example 1.17.10 Asymptotes: rational function
