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Aug 31, 2024
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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 piece-wise functions)
- Compare and contrast transformations
- Create functions using standard function operations
- Describe an inverse function
- Manipulate a one-to-one function to create an inverse function
- Evaluate polynomial functions
- Analyze a polynomial function and relate it to a real-world application
- Rewrite a quadratic function in standard form
- Find the vertex and any x-intercepts 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 right-triangle definition of the trigonometric functions
- Solve mathematical and real-life right triangle problems
- Apply the Law of Cosines to mathematical and real-life problems
- Apply the Law of Sines to mathematical and real-life problems
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