Center for Curriculum and Transfer Articulation
College Algebra/Functions
Course: MAT150

First Term: 2017 Summer
Lecture   5 Credit(s)   5 Period(s)   5 Load  
Course Type: Academic
Load Formula: S - Standard Load


Description: Analysis and interpretation of the behavior and nature of functions including polynomial, rational, exponential, logarithmic, power, absolute value, and piecewise-defined functions; systems of equations, using multiple methods including matrices, modeling and solving real world problems, and defining and illustrating sequences and series.



MCCCD Official Course Competencies
1. Define, distinguish, and interpret the relations and functions and their inverses represented verbally, graphically, numerically, or algebraically. (I-VII)
2. Calculate and interpret the average rate of change in varied contexts, using function notation including the difference quotient. (I)
3. Evaluate functions and solve function equations and inequalities using multiple methods. (I-VII)
4. Set up, solve, and interpret the meaning of solutions of systems of linear and nonlinear equations and inequalities using multiple methods, including matrices where appropriate. (VIII)
5. Identify, graph, analyze, and determine the key characteristics of the following function types and their transformations: polynomial, power, radical, rational, exponential, logarithmic, absolute value, piecewise-defined, and discrete. (I-VII)
6. Model real world situations using a variety of mathematical techniques (including regression) and solve real world mathematical problems using functions and function compositions. (I-IX)
7. Introduce sequences and series. (IX)
 
MCCCD Official Course Outline
I. Functions
   A. Make sense of relations and functions represented verbally, graphically, numerically, or algebraically
   B. Evaluate functions
   C. Operations on functions including composition
   D. Key characteristics of functions, when applicable, include, end behavior, intercepts, increasing/decreasing, concavity, asymptotes, domain and range, and extrema
   E. Average rate of change using function notation and the difference quotient
   F. Applications

II.Transformations of functions
   A. Vertical/horizontal shifts
   B. Reflections
   C. Scaling
   D. Applications

III. Inverse functions
   A. Inverse function notation
   B. One-to-one
   C. Domain and range
   D. Evaluating and solving
   E. Applications

IV. Exponential functions
   A. Evaluating
   B. Key characteristics of functions, when applicable, include, end behavior, intercepts, increasing/decreasing, concavity, asymptotes, domain and range, and extrema
   C. Graphing
   D. Applications

V. Logarithmic functions
   A. Evaluating and solving logarithmic equations
   B. Key characteristics of functions, when applicable, include, end behavior, intercepts, increasing/decreasing, concavity, asymptotes, domain and range, and extrema
   C. Graphing
   D. Use to solve exponential equations
   E. Applications

VI. Polynomial functions
   A. Evaluating and solving equations and inequalities
   B. Key characteristics of functions, when applicable, include, end behavior, intercepts, increasing/decreasing, concavity, asymptotes, domain and range, and extrema
   C. Graphing
   D. Applications

VII. Rational functions
   A. Evaluating and solving equations and inequalities
   B. Key characteristics of functions, when applicable, include, end behavior, intercepts, increasing/decreasing, concavity, asymptotes, domain and range, and extrema
   C. Graphing
   D. Applications

VIII. Systems of linear and nonlinear equations and inequalities
   A. Set up and solve using multiple methods
   B. Interpret the meaning of solutions

IX. Introduction to sequences and series
   A. Summation notation
   B. Arithmetic
   C. Geometric

 
MCCCD Governing Board Approval Date: February 28, 2017

All information published is subject to change without notice. Every effort has been made to ensure the accuracy of information presented, but based on the dynamic nature of the curricular process, course and program information is subject to change in order to reflect the most current information available.