Algebraic Functions 2

Students will learn and apply algebraic concepts to solve real-world problems.
Prerequisite: Functions 1

Students will be helped to visualize, represent, model and solve problems that involve applications with business and science as well as make connections within the field of mathematics. The focus of the course will include topics such as quadratic, polynomial, rational, radical, and exponential functions.

1. Polynomial Functions
a. Sums, Difference and Products of linear functions
i. Symbolically
ii. Graphically
b. Behavior of graphs
c. Quadratic Functions
i. Graphs
1. Key Characteristics (Maximum, minimum, intercepts, symmetry, vertex, end-behavior)
2. Domain and Range
3. Standard Form
4. Vertex Form
a. Translations, reflections and dilations
ii. Solving Equations
1. By Factoring
2. Using Roots
3. Quadratic Formula
a. Complex Numbers
d. Sums, Differences and Products of linear and non-linear functions
i. Symbolically
ii. Graphically
1. Key Characteristics [degree, maximum, minimum, intercepts, symmetry (even or odd), end-behavior]
2. Domain and Range
iii. Be able to write the equation of a polynomial function given the degree and information about its roots
iv. Solving Polynomial Equations
1. Graphing (technology)
2. Factoring cubic equations

2. Rational Functions
a. Symbolically
b. Graphically
1. Key Characteristics (Maximum, minimum, intercepts, symmetry, vertex, end-behavior)
2. Domain and Range

3. Radical Functions
a. Symbolically
b. Graphically
1. Key Characteristics (Maximum, minimum, intercepts, symmetry, vertex, end-behavior)
2. Domain and Range

4. Exponential Functions
a. Symbolically
b. Graphically
1. Key Characteristics (Maximum, minimum, intercepts, symmetry, vertex, end-behavior)
2. Domain and Range

5. Combinations of Functions
a. Composition
b. Inverse
c. Combinations

6. Sequences and Series
a. Arithmetic
1. Explicit formula
2. Recursive formula
3. Sums of finite series
b. Geometric
1. Explicit formula
2. Recursive formula
3. Sums of finite series
c. Sigma Notation