What is a Function?
Objectives: Upon completion of the unit, students will be able to:
 Evaluate functions
 Perform algebraic manipulations on functions
 Determine a maximum or minimum of a function to determine intervals of increase and decrease
 Find the domain and range of a function
 Interpret and graph a piece-wise function
 Find and evaluate composite functions
 Determine maximum and minimum in application problems
 Find average rate of change given a function, table of values or a graph
 Evaluate the difference quotient
 Determine transformations from a graph, table or function
 Find and graph the inverse of a function

Systems of Equations and Inequalities

Objectives: Upon completion of the unit, students will be able to:
 Solve a system using the graphing, substitution and elimination method
 Determine if a system is dependent, independent or inconsistent
 Set up and solve an application using a system
 Solve a system involving two or three variables, including writing the variables in terms of a parameter
 Find an augmented matrix to represent a system of equations
 Solve a system using RREF or REF, and using matrices
 Perform matrix operations algebraically and on graphing calculator
 Find determinant of a matrix, and find the inverse of a matrix
 Set up and solve a partial fraction decomposition problem
 Solve a non-linear system

Polynomial and Rational Functions

Objectives: Upon completion of the unit, students will be able to:
 Complete the square to write a quadratic in standard form
 Determine maximum and minimum values of a polynomial
 Determine intervals of increase and decrease in a polynomial function
 Solve a quadratic equation
 Divide a polynomial into another to determine remainder of a function or factor of a function
 Factor a polynomial
 Find all zeros of a polynomial (real, complex, rational, irrational, etc.)
 Simplify complex numbers using various algebraic techniques
 Use the graphing calculator to SUPPLEMENT your algebraic work throughout the chapter
 Identify and prove lower and upper bound of a polynomial or graph
 Use Descartes Rule of Signs to determine how many positive or negative zeros are possible
 Graph rational function
 Find asymptotes (VA, HA, SA), intercepts and/or holes of rational functions

Exponential and Logarithmic Functions

Objectives: Upon completion of the unit, students will be able to:
 Sketch a graph of an exponential growth, exponential decay, logarithmic and natural logarithm functions
 Solve and set up an application problem involving exponential and logarithmic functions
 Covert from logarithmic to exponential and vice versa
 Evaluate logarithms without a calculator
 Use properties of logarithms to simplify (condense) or expand an expression
 Use Change of Base formula to calculate logs other than common logs or natural logs
 Solve exponential equations and logarithmic equations
 Determine domain and range of logarithmic functions and exponential functions

Trigonometry
Objectives: Upon completion of this unit, students will be able to:
 Convert angles from degrees to radians and vice versa
 Find coterminal angles and use those angles in the unit circle
 Locate and draw reference triangles, using the angle in standard position
 Solve a right triangle (find all 3 sides and all 3 angles)
 Determine the trig functions of a particular angle using the unit circle
 Find exact values of trig functions of the reference triangles of multiples of pi/6, pi/4 or pi/3 (finding terminal point)
 Solve applications involving right triangles
 Use symmetry about the unit circle to find exact trig values
 Graph all 6 trig functions on the coordinate plane (and identify zeros, asymptotes, etc.)
 Write trigonometric functions based on application information (ferris wheel type, harmonic motion, etc.)
 Use Law of Sines and Law of Cosines to solve non-right triangles and their applications
 Use inverse trig to evaluate expressions


Trigonometric Identities and Solving Trig Equations

Objectives: Upon completion of the unit, students will be able to:
 Simplify trigonometric expressions involving trig identities
 Use trig identities to determine the exact value of an expression
 Solve trig equations (use trig identities, zero product property, using triangles, inverse trig, etc.)

  Conic Sections

  Objectives: Upon completion of the unit, students will be able to:
 Name all conic sections (circle, ellipse, parabola, hyperbola)
 Graph each of the conic sections, labeling all important parts
 Determine the standard form of each conic section
 Find information such as center, vertices, foci, eccentricity, asymptotes and directrix
 Find an equation given specific points or lengths
 Determine what type of conic section it is by looking at general form
 Use completing the square to write a conic section in standard form, and to aid in determining what type of conic it is

  Binomial Theorem and Pascal's Triangle