Topics and Objectives:

1. Factoring Polynomials/Rational Expression Operations

— Factor second-degree polynomials

— Factor by grouping

— Reduce rational expressions to lowest terms

— Add/subtract/multiply /divide rational expressions

— Simplify compound fractions

2. Using Graphing Calculators

— understand screen coordinates

— use the Trace, Zoom, and Intersect commands

3. Functions

— Identify functions vs relations in tables, graphs, and equations

— Use function notations interchangeably and identify the domains and ranges

— Solve equations and formulas for a variable

— Identify increasing and decreasing functions

— find local maxima and minima

— Define functions piecewise

— Shift graphs horizontally and vertically

— Stretch and shrink graphs

— Reflect graphs in the x and y axis

— Perform operations on functions

— Find the composition of two functions

— Find the inverse of a function

— Graph the inverse of a function

4. Linear Functions

— Use slope-intercept and linear combination forms in problem solving

— Fit a linear model to to a situation or data

— Explore the graph Ax + By = C

— Define the slope of a line

5. Quadratic Functions

— Solve quadratic equations for real and complex solutions using the square root method, factoring and the Quadratic Formula.

— Fit a quadratic model to data using the graphing calculator.

— Perform operations with complex numbers and analyze the solutions and x-intercepts of quadratics using the discriminant

— Use the vertex form of a quadratic function

— Solve equations involving radicals

— Solve equations of quadratic type

— Solve linear and quadratic inequalities

6. Polynomial and Rational Functions

— Analyze graphs of polynomials

— Divide polynomials using long and synthetic division

— Apply the Remainder and Factor theorems

— Approximate real zeros at turning points

— Solve polynomial inequalities

— Find vertical and horizontal asymptotes of Rational functions

— Draw the graph of a Rational function

— Solve Rational inequalities

— Find factors of polynomials with real coefficients

— Find rational zeros

— Model using Direct variation

— Model using Inverse variation

7. Exponential and Logarithmic Functions

— Evaluate logarithmic expressions and solve logarithmic equations.

— Apply properties of logarithms to solving exponential and logarithmic equations and applications.

— Apply exponential growth and decay models (including continuous growth) to problem solving.

— Define exponential functions

— Analyze graphs of exponential functions including Base e

— Calculate compound interest (including continuous interest)

— Write an equation that models exponential growth or negative exponential growth

— Apply the change-of-base formula

— Solve problems using a logarithmic scale

8. Systems of Equations

— Solve systems of equations in two variables using graphing, substitution, linear combination.

— Solve systems of equations in three variables using elimination by addition

9. Basic Formulas of Analytic Geometry

— Apply basic formulas of Analytic Geometry