Topic Outline

Topical Outline 

Functions, Linear Functions (Chapter 1 Big Ideas Textbook)

I.   Modeling with Linear Functions

a. Writing Linear Functions

b. Linear Regression

c. Piecewise Functions

II. System of Equations

a. Two Variable Systems

b. Three Variable Systems

II. Parent Functions and Transformations

a. What are Parent Functions

b. Transformations of Parent Functions

Characteristics of Quadratic Functions (Chapter 2 Big Ideas Textbook)

I. Transformations of Quadratic Functions

II. Key Characteristics of a Quadratic Functions

a. What are the zeros

b. Line of Symmetry

c. Vertex

d. Domain and Range

III. Modeling with Quadratics

Solving Quadratic Equations (Chapter 3 Big Ideas Textbook)

I. Solving Quadratic Equations - Review Factoring

a. Solving with Factoring

b. Solving with taking the square root

c. Solving by completing the square

d. Solving with the Quadratic Formula

II. Complex Numbers

a. What is a complex number

b. How to simplify complex numbers

 Polynomials (Chapter 4 Big Ideas Textbook)

I. Graphs of Polynomials

a. Degree of Polynomials

b. End Behavior

c. Zeros

d. Domain and Range

II. Operations of Polynomials

a. Adding, Subtracting, and Multiplying Polynomials

b. Division of Polynomials

i. Long Division

ii. Synthetic Division

c. Factoring Polynomials

III. Fundamental Theorem of Algebra

Rational Exponents and Radical Functions (Chapter 5 Big Ideas Textbook)

I. nth Root and Rational Exponents

II. Properties of Exponents and simplifying 

a. Simplifying Rational Exponents

b. Simplifying Radicals

III. Solving Radical Equations

IV. Graphing Radical Functions

a. Critical points in the graph

b. Domain and Range 

Inverse Functions (Chapter 5.6 Big Ideas Textbook)

I. What is an Inverse

II. How to find the Inverse

III. Verify the Inverse

Rational Functions (Chapter 7 Big Ideas Textbook)

 I. Graphs of Rational Functions

a. Vertical and Horizontal Asymptotes

b. Domain and Range

II. Simplifying Rational Expression

a. Multiplying and Dividing Rational Expressions

c. Adding and Subtracting Rational Expressions

III. Solving Rational Equations

a. Solving Proportions

b. Solving by clearing the Fractions

 Exponential/Logarithmic Functions (Chapter 6 Big Ideas Textbook)

I. Exponential Functions

a. Writing Exponential Functions

b. Graphing Exponential Functions

II. Natural base Functions

a. What is the natural base

b. Graph of the natural base

II. Logarithmic Functions

a. Graphing Logarithmic Functions

b. Domain and Range

III. Solving Equations

a. Solving Exponential with same base

b. Using the Logarithmic Properties to solve