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||Title:||College Algebra: MA1
||Long Title:||College Algebra: GT-MA1
||Course Description:||Focuses on a variety of functions and the exploration of their graphs. Topics include: equations and inequalities, operations on functions, exponential and logarithmic functions, linear and non-linear systems, and an introduction to conic sections. This course provides essential skills for Science, Technology, Engineering, and Math (STEM) pathways.
This is a statewide Guaranteed Transfer course in the GT-MA1 category.
||Status Notes:|| Replaced by MAT 160 in Fall 2000? Note: Competencies and
|| ||S: Outline entered from Core Transfer Documents. A new
|| ||S: course template exists and will be submitted for review.
||Origin Notes:|| ACC
||General Notes:||MPM Updates 3/28/2018
||Course Notes:|| updated new GT language 8/7/18 dl
For REQUIRED SYLLABUS information that is to be included on all syllabi starting Spring 2018, 201830 go to https://internal.cccs.edu/wp-content/uploads/documents/GT-MA1-Required-Syllabus-Info.docx.:
1. Identify properties of functions including domain, range, increasing and decreasing.
2. Apply function notation.
3. Determine the inverse of a function.
4. Examine functions algebraically.
5. Analyze behavior and roots of polynomial functions.
6. Solve polynomial, rational and absolute value equations and inequalities.
7. Analyze polynomial, exponential, logarithmic and rational functions.
8. Create graphs of polynomial, exponential, logarithmic and rational functions.
9. Solve exponential and logarithmic equations.
10. Analyze piecewise functions.
11. Graph parent functions and their transformations.
12. Utilize algebraic techniques to solve application problems.
13. Solve systems of equations.
14. Classify conic sections.
REQUIRED TOPICAL OUTLINE
I. Functions including domain, range, increasing and decreasing
A. Definition of a function
B. Identifying functions given table, graph or equation form
C. Domain and range of algebraic functions
D. Even and odd functions
E. Introduction to where functions are increasing and decreasing using a graph
F. Introduction to maxima and minima using a graph
II. Function notation
A. Functions expressed using function notation
B. Evaluation of function notation from equations and graphs
C. Difference quotient
III. Inverse of a function
A. Notation of an inverse function
B. Definition of one-to-one functions
C. Algebraic determination of the inverse of a function
D. Graphical properties of an inverse function
E. Domain and range of an inverse function
IV. Function composition algebraically
A. Sum difference, product, quotient of functions
B. Composition notation
C. Inverses using composition
D. Composition of two functions
E. Domain of a composite function
F. Decomposition of a function
V. Behavior and roots of polynomial functions
A. End behavior of polynomial functions
B. Division of polynomials
C. Polynomials as a product of linear factors
D. Multiplicity of zeros
E. Complex zeros
F. The Rational Root Theorem
G. The Remainder Theorem and the Factor Theorem
VI. Polynomial, rational and absolute value equations and inequalities
A. Completing the square to find the vertex form of a quadratic function
B. Absolute value inequalities
C. Polynomial and rational inequalities using test intervals (critical values, number lines)
D. Methods of solving quadratic equations
E. Solving equations reducible to quadratic form using substitutions
F. Review of solving rational equations
VII. Analysis of polynomial, exponential, logarithmic and rational functions
A. Intercepts and End behavior
C. Definition of exponential and logarithmic functions
D. Domain and range
E. Evaluation of exponential and logarithmic expressions
F. Introduction to the number e
G. Equations of asymptotes
VIII. Graphs of polynomial, exponential, logarithmic and rational functions
A. Intercepts and end behavior
B. Asymptotes of functions from the equation and from the graph
C. Identifying the removable discontinuities of a rational function
D. Determining if a graph crosses horizontal asymptotes
IX. Solutions of exponential and logarithmic equations
A. Conversion between exponential and logarithmic form
B. Properties of logarithms
C. Logarithmic equations
D. Extraneous solutions
E. Exponential equations
F. Change of base formula
X. Piecewise functions
A. Notation for piecewise functions
B. Evaluation of piecewise functions
C. Graphs of piecewise functions
D. Domain of piecewise functions
XI. Parent functions and their transformations
A. Parent (also called base/toolbox) functions
B. Rigid transformations (horizontal/vertical translations and reflections)
C. Non-rigid transformations (horizontal/vertical scaling)
XII. Algebraic techniques to solve application problems
A. Quadratic models including optimization
B. Exponential/logarithmic models
C. Direct and inverse variation
XIII. Systems of equations
A. Methods for solving systems with three variables or more
B. Systems of non-linear equations with two variables
C. Types of solutions (consistent, inconsistent, independent and dependent)
XIV. Conic sections
E. Analysis of the properties of conic sections
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