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Dec 12, 2024
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MAT 121 - College Algebra Credits: 4 Lecture Hours: 4 Lab Hours: 0 Practicum Hours: 0 Work Experience: 0 Course Type: General This course provides an intensified study of algebraic techniques and prepares students for future study in mathematics. The central theme of this course is the concept of a function and its graph. Topics include: linear functions, polynomial functions, piece-wise functions, rational functions, radical functions, exponential/logarithmic functions, and systems of equations. Prerequisite: Minimum ALEKS scores of 46% or MAT 073 with a C- or better Competencies
- Analyze equations, inequalities, and mathematical models
- Graph equations and inequalities
- Solve linear, quadratic, polynomial, rational, radical, and absolute value equations
- Model real-world situations through mathematics
- Simplify complex numbers
- Evaluate functions
- Calculate slope of linear functions
- Calculate midpoint and distance between two points
- Determine domain and range
- Utilize vertical line test
- Distinguish properties of functions (including piece-wise functions)
- Compare and contrast functions and their transformations
- Analyze combinations of functions
- Describe inverse functions
- 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
- Use Gaussian elimination to calculate matrix solutions to linear systems
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