MAT 129  Precalculus Credits: 5 Lecture Hours: 5 Lab Hours: 0 Practicum Hours: 0 Work Experience: 0 Course Type: Core The central theme of this course is the concept of a function and its graph. Topics include: functions (linear, radical, exponential, logarithmic, polynomial, piecewise and trigonometric) and their graphs, and basic trigonometry. Prerequisite: Minimum ALEKS scores of 61% or MAT 130 with a C or better Competencies
 Analyze mathematical functions
 Describe a function
 Determine if a relation is a function
 Analyze the function to determine the domain and range of a function
 Determine minimum and maximum values of a function
 Analyze a function to determine whether functions are increasing, decreasing or constant
 Categorize whether functions have even or odd properties
 Evaluate functions
 Examine and graph common functions (including piecewise functions)
 Compare and contrast transformations
 Create functions using standard function operations
 Describe an inverse function
 Manipulate a onetoone function to create an inverse function
 Evaluate polynomial functions
 Analyze a polynomial function and relate it to a realworld application
 Rewrite a quadratic function in standard form
 Find the vertex and any xintercepts of a graph of a quadratic function
 Determine real and complex zeros of a polynomial function
 Utilize the fundamental Theorem of Algebra
 Apply the intermediate value, remainder, factor, and rational root theorems to find polynomial roots
 Examine and graph polynomial functions
 Interpret inequalities involving polynomial functions
 Evaluate rational functions
 Analyze a rational function
 Determine horizontal/vertical/oblique asymptotes and any removable discontinuities
 Examine and graph a rational function
 Interpret inequalities involving rational functions
 Evaluate exponential functions
 Analyze exponential functions
 Examine and graph exponential functions
 Solve exponential equations
 Evaluate logarithmic functions
 Analyze logarithmic functions
 Apply the properties of logarithms
 Examine and graph logarithmic functions
 Solve logarithmic equations
 Apply exponential and logarithmic functions to problems involving interest, growth and decay
 Solve systems of equations
 Calculate and interpret solutions of linear systems
 Perform partial fraction decomposition
 Utilize matrices and determinants
 Compute matrix solutions to linear systems using Gaussian elimination
 Perform matrix operations
 Calculate multiplicative inverses
 Identify and solve matrix equations
 Interpret angles and their measure
 Draw angles whose measures are given in degrees and radians
 Determine a positive angle less than one revolution that is coterminal with a given angle
 Use radian measure of angles
 Convert degree measure to radian measure
 Convert radian measure to degree measure
 Establish the trigonometric functions on a unit circle
 Determine sine, cosine, and tangent using the unit circle
 Determine the reciprocal functions using the unit circle
 Make sense of the eight fundamental identities
 Use the fundamental identities to simplify trigonometric expressions
 Evaluate trigonometric functions using the fundamental identities
 Determine the values of trigonometric functions
 Identify the signs of the trigonometric functions by quadrant
 Assess trigonometric functions
 Interpret the generalized definition of the trigonometric functions
 Evaluate the trigonometric functions given a point on the terminal side
 Find the reference angle for any given triangle
 Evaluate trigonometric functions of real numbers by table/calculator
 List the exact values for the trigonometric functions pi/6, pi/4, pi/3, pi/2, pi
 Analyze the trigonometric functions using a table/calculator
 Determine the domain and range
 Graph trigonometric functions
 Sketch the standard forms of the cosine, sine, tangent, secant, cosecant, and cotangent curves from memory
 Graph by plotting points
 Analyze and sketch trig functions using: amplitudes, periods, and phase shifts
 Investigate trigonometric identities.
 Apply half angle, double angle, and sum/difference trigonometric identities to write equivalent forms of expressions
 Find exact values by using half angle, double angle, and sum/difference trigonometric identities
 Solve trigonometric equations
 Solve linear and quadratic trigonometric equations
 Solve quadratic trigonometric equations
 Assess inverse trigonometric functions
 Define inverse trigonometric relations and functions
 Evaluate inverse functions including domain and range
 Investigate the right triangle definition of the trigonometric function
 Use the righttriangle definition of the trigonometric functions
 Solve mathematical and reallife right triangle problems
 Apply the Law of Cosines to mathematical and reallife problems
 Apply the Law of Sines to mathematical and reallife problems
Add to Portfolio (opens a new window)
