Course Outline for College Algebra

Catalog description (2006-2009 Catalog):

In-depth study of linear and quadratic functions, their graphs and transformations; inverse
functions; modeling; polynomial functions and their graphs; and conic sections. The
graphing calculator will be used throughout the course. 4 lecture hours

Is the course New, Revised or Modified? Revised

Required texts/other materials

1. Text: College Algebra: An Early Functions Approach, by Blitzer
Publisher: Pearson Prentice-Hall
2. Calculator: A graphing calculator is required. Recommended: TI-83, 84 or 86.
Calculators with symbolic manipulation are not permitted.

Information resources:
• The college library has many books, CDs and videos available.
• MyMathLab is an on-line companion to the text offering a lot of practice.
• The Learning Center has tutoring and help available to the students.

Course Competencies/Goals:

Students will be able to demonstrate the ability to:

A. recognize and work with functions and function notation.
B. determine the inverse of a function, if it exists, and the relationship that exists between
and function and its inverse both algebraically and graphically.
C. solve algebraically and graphically linear and quadratic equations and inequalities.
D. explain the relationship of real numbers to complex numbers and perform algebraic
operations with complex numbers.
E. recognize common graphs, graphing transformations and find pertinent information from
the graphs.
F. define a polynomial and explain the characteristics of the graph of a polynomial
including end behavior, degree and multiplicity of zeros.
G. perform the algebra of functions including the composition of functions.
H. recognize algebraically and graphically the conic sections and find pertinent information
about them.
I. demonstrate expertise in sketching functions and in using the graphing calculator to graph
functions, to enter expressions on which mathematical operations are to be performed
properly, and to find a linear or quadratic regression for given data.
J. solve word problems (or models).

Course-specific General Education Knowledge Goals and Core Skills:

General Education Knowledge Goals:

Goal 1. Communication. Students will communicate effectively in both speech and
writing.
Goal 2. Mathematics. Students will use appropriate mathematical and statistical
concepts and operations to interpret data and to solve problems.
Goal 4. Technology. Students will use computer systems or other appropriate forms of
technology to achieve educational and personal goals.

MCCC Core Skills:

Goal A. Written and Oral Communication in English. Students will communicate
effectively in speech and writing, and demonstrate proficiency in reading.
Goal B. Critical Thinking and Problem-solving. Students will use critical thinking and
problem solving skills in analyzing information.

 In the following Units of Study in Detail Course Competencies/Goals will be denoted
CG, General Education Knowledge Goals will be denoted GE, and MCCC Core
Skills will be denoted CS.

Units of Study in Detail:

Unit I – Functions and Graphs - Approximately 5 weeks

The student will be able to:

1. define and use properly in written and oral communication all of the vocabulary presented in
this unit. (CG A; GE 1,2; CS A)
2. sketch graphs of equations by point plotting and by using a graphing calculator. (CG C,I;
GE 1,2; CS A,B)
3. use graphs of equations to solve application problems. (CG C,J; GE 2, 4; CS B)
4. find the slopes of lines and use slope to identify parallel and perpendicular lines. (CG C,J;
GE 2; CS B)
5. write linear equations given points on lines and their slopes. (CG C,J; GE 1,2; CS A,B)
6. use slope intercept forms of linear equations to sketch lines. (CG C,J; GE 2; CS A,B)
7. find x- and y- intercepts of graphs of equations. (CG E,J; GE 2; CS B)
8. find solutions of equations graphically. (CG C,I; GE 2; CS B)
9. find the points of intersection of two graphs. CG C,I; GE 2; CS B)
10. decide whether a relation between two variables identifies a function. (CG A: GE 2; CS A,B)
11. use function notation, evaluate functions and find the domains and ranges of functions.
(CG A; GE 2; CS A,B)
12. use functions to model and solve application problems. (CG A, J; GE 2; CS B)
13. evaluate difference quotients. (CG A; GE 2; CS B)
14. use the vertical line test for to determine if a graph represents a functions. (CG A; GE 2;
CS B)
15. determine from its graph intervals on which function is increasing, decreasing or constant.
(CG A,I; GE 2; CS B)
16. determine relative maximum and minimum values of quadratic functions. (CG A,E,I; GE 2:
CS B)
17. identify and graph piecewise functions. (CG A,E,I; GE 2; CS B)
18. identify even and odd functions. (CG A,G; GE 2; CS 2)
19. recognize graphs of common functions. (CG A,E;GE 2; CS B)
20. use vertical and horizontal shifts, reflections and non-rigid transformations to graph
functions. (CG E, I; GE 2; CS A,B)
21. add, subtract, multiply and divide functions. (CG A,E,G; GE 2; CS B)
22. find compositions of one function with another function. (CG A,E,G; GE 2; CS B)
23. use combinations of functions to model and solve application problems. (CG A,E,G,J; GE 2; CS B)
24. find inverse functions and verify that two functions are inverses of each other. (CG A,B,E,G; GE 2;
CS A,B)
25. determine graphically and algebraically whether a function has an inverse. (CG A,B; GE 2;
CS A,B)
26. determine if functions are 1-1 and, if not, how to restrict the domains so that they are. (CG A,
B,G; GE 2; CS A,B)
27. find inverse functions, if they exist, algebraically. (CG A,B,G; GE 2; CS B)