111.35.P.1: The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise-defined functions.

111.35.P.1.A: describe parent functions symbolically and graphically, including f(x) = x to the n power, f(x) = 1n x, f(x) = loga x, f(x) = 1/x, f(x) = e to the x power, f(x) = |x|, f(x) = a to the x power, f(x) = sin x, f(x) = arcsin x, etc.;

Absolute Value with Linear Functions
Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Translating and Scaling Functions

111.35.P.1.B: determine the domain and range of functions using graphs, tables, and symbols;

Exponential Functions
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Logarithmic Functions
Radical Functions

111.35.P.1.D: recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function; and

Logarithmic Functions

111.35.P.1.E: investigate the concepts of continuity, end behavior, asymptotes, and limits and connect these characteristics to functions represented graphically and numerically.

Exponential Functions
General Form of a Rational Function
Logarithmic Functions
Zap It! Game

111.35.P.2: The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful problems.

111.35.P.2.A: apply basic transformations, including a ? f(x), f(x) + d, f(x - c), f(b ? x), and compositions with absolute value functions, including |f(x)|, and f(|x|), to the parent functions;

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

111.35.P.2.B: perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, and graphically; and

Function Machines 1 (Functions and Tables)

111.35.P.2.C: investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties.

Cosine Function
Exponential Functions
Sine Function
Tangent Function

111.35.P.3: The student uses functions and their properties, tools and technology, to model and solve meaningful problems.

111.35.P.3.A: investigate properties of trigonometric and polynomial functions;

Graphs of Polynomial Functions

111.35.P.3.B: use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;

Compound Interest
Linear Functions

111.35.P.3.D: use properties of functions to analyze and solve problems and make predictions; and

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Points, Lines, and Equations

111.35.P.3.E: solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.

Sine, Cosine, and Tangent Ratios

111.35.P.4: The student uses sequences and series as well as tools and technology to represent, analyze, and solve real-life problems.

111.35.P.4.A: represent patterns using arithmetic and geometric sequences and series;

Arithmetic Sequences
Geometric Sequences

111.35.P.4.B: use arithmetic, geometric, and other sequences and series to solve real-life problems;

Arithmetic and Geometric Sequences

111.35.P.4.D: apply sequences and series to solve problems including sums and binomial expansion.

Arithmetic Sequences
Geometric Sequences

111.35.P.5: The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations.

111.35.P.5.A: use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets;

Circles