College Algebra/Functions with Review
 Course: MAT156 First Term: 2019 Fall Final Term: Current Final Term: 2020 Spring Lecture   6.0 Credit(s)   6.0 Period(s)   6.0 Load       Credit(s)    Period(s)    Load Subject Type: Academic Load Formula: S- Standard

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-X)
MCCCD Official Course Competencies must be coordinated with the content outline so that each major point in the outline serves one or more competencies. MCCCD faculty retains authority in determining the pedagogical approach, methodology, content sequencing, and assessment metrics for student work. Please see individual course syllabi for additional information, including specific course requirements.

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
X. Review of selected topics from MAT12+ Intermediate Algebra as needed throughout the course. These topics may also be placed throughout the outline as they are deemed necessary.

MCCCD Governing Board Approval Date: January 22, 2019

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.