Mercer County Community College/ Liberal Arts Division/ Mathematics Department

Course: MAT 145                    Precalculus for Business or Social Sciences                 

Catalog Description: A second course in the mathematics sequence leading to business or social sciences calculus.  Topics include polynomial, rational, and piecewise defined functions, equations and inequalities: exponential and logarithmic functions and their graphs; multivariable systems of equations and matrices; extensive use of modeling and graphing calculators.

Prerequisites:        MAT141 with minimum C grade


Instructor:  Richard Porter    


Contact Info:   E-mail: porterr@mcc.ecu

Web Page:

Office: LA 114  Extension 3826

                        Office Hours:  See Web Page

Book:  Precalculus, 6th edition

            by Larson and Hostetler

            Houghton Mifflin Publishers

Graphing Calculator: TI-83 or 86 recommended

            TI 89 or 92 NOT permitted


Course Info: 


Grading:                                                                           Grade Scale:

Quizzes (10 quizzes 1% each)       10%

Regression Project                         10%

EXAMS (2 exams, 10 % each)      20%

Midterm                                         20%

Final:                                               40%








Attendance: Perfect attendance is expected, and students are responsible for all material covered. Arriving late or leaving early will count as missing HALF a class. Any student missing the equivalent of 4 classes is not eligible to receive credit for the course. If a WI grade is appropriate it will be given, if not, the student will receive an F. No excuse will be considered if it is not presented in writing and produced in advance when possible.


Make-ups: No make-ups are given for any reason. When valid excuses are produced in writing, work may be replaced by equivalent work from the final exam. One quiz can be missed without excuse.


Quizzes: Students should expect to hand in homework every class. The quiz grade will be made of questions from the homework or lecture. For all quizzes, the homework may be used as reference for the quiz, so do your homework! Homework is not accepted late.


Regression Project:  A modeling project will be assigned during the semester. It will require the choosing of a relevant topic, the collection of data, the creation of a function to model the data, a graph of the data, a useful prediction.


Exams: There will be two exams, a midterm, and a final. The timed midterm and final will be administered in class. The two exams will be given at the testing center with no time limit. Each exam is usually about 10 to 20 short answer questions. There are NO multiple choice questions, showing all work is required even for calculator problems, and partial credit is given for correct work shown on exam. No scrap paper, books, notes, formulas, or calculator programs may be used with the exam.




Academic Integrity: Students are encouraged to work together on homework. Students are expected to do their own work. Students who are caught cheating on tests will fail the course.


Classroom: Do not smoke or eat in class. No visitors (especially children) may attend. Disruptive students are expected to leave. Cell phones, beepers, and pagers can be disruptive and must be silent.










T 1/20

Introduction to Graphs and Equations






R 1/22

Data and Functions






T 1/27

Transformations of Functions






R 1/29

Combinations of Functions





T 2/3

Inverse Functions and Solving Equations





R 2/5






T 2/10

Review Exam 1





R 2/12

Intro to Polynomial Functions





T 2/17

Higher degree Polynomial Functions





R 2/19

Polynomial Division and Complex Numbers






T 2/24

Zeros of Polynomials and Graphing





R 2/26

Rational Functions





T 3/2

Exponential Functions





R 3/4

Logarithmic Functions





T 3/9

Review Midterm





R 3/11

In Class Midterm





T 3/23

Review of Logs and Exponents





R 3/25

Solving Log Equations





T 3/30

Applications of Logs and Exponents





R 4/1

Discussions of Projects





T 4/6

Systems of Equations






R 4/8

Multivariable Systems






T 4/13

Review Exam 2





R 4/15

Systems of Inequalities





T 4/20

Linear Programming





R 4/22

Matrices and Equations





T 4/27

Matrix Operations







R 4/29

Applications of Matrices





T 5/4

Other Applications of Precalculus





R 5/6

Review for Final Exam





T 5/11

Final Exam




Course Objectives


Answer the questions:

  1. Why are you taking this course? Because it is required.
  2. Why is the course required for your major? Because the field uses functions.
  3. What are functions? Representations of how one variable affects another.
  4. How are the ways that functions can be represented? Points, equations, graphs.
  5. How can data be turned into equations? Modeling or Regressions
  6. How can equations be turned into graphs? Plotting, technology, graphing techniques
  7. How can equations and graphs be used to make predictions? Evaluating, solving, interpreting, technology, and techniques.
  8. How good are the predictions? What do you think of others’ predictions?
  9. What is calculus? The study of change.
  10. How are you prepared for calculus and everyday living?



Define, state, or identify:

You should be able to:


1.        graph of an equation

2.        intercepts

3.        symmetry

4.        linear equations in 2 variables

5.        slope

6.        slope intercept form of a linear equation

7.        point slope form of a linear equation

8.        general form of a linear equation

9.        parallel lines

10.     perpendicular lines

11.     relation

12.     function

13.     domain

14.     range

15.     independent variable

16.     dependent variable

17.     function notation

18.     implied domain

19.     vertical line test

20.     zeros, roots and solutions of a function

21.     relative minimum

22.     relative maximum

23.     symmetry in even functions

24.     symmetry in odd functions

25.     vertical and horizontal shifts of a graph

26.     stretches and compressions of a graph

27.     reflections of a graph about the x or y axes

28.     inverse functions, notation and symmetry

29.     horizontal line test

30.     one to one function

31.     direct proportion or variation

32.     inverse variation

33.     joint variation


1.        sketch the graph of an equation and confirm the sketch by choosing an

appropriate viewing window on the graphing calculator

2.        find the intercepts, symmetry, domain, and range, identify types of symmetry and confirm each on the graphing calculator

3.        make a table of values on the graphing calculator for a given equation

4.        write the equation of a circle in standard form given its center and a point on the circle and sketch the graph

5.        find the slope of a line and use it to graph the line

6.        use slope to identify parallel or perpendicular lines

7.        write the equation of a line when given a point on the line and its slope or two points on the line

8.        write a linear equation in slope intercept or standard form

9.        determine whether a relation is a function when given a set of ordered pairs, an equation, or a graph

10.     use function notation to evaluate functions

11.     determine the domain and range of a function and the implied domain, if applicable

12.     evaluate a difference quotient given in function notation when given the function

13.      find the zeros, roots and solutions of a function

14.     determine the intervals where the function is increasing, decreasing, or constant

15.     identify even or odd functions

16.     find relative extrema for a given function and confirm by using the maximum or minimum functions on the graphing calculator

17.     recognize the equations and graphs of basic types of functions such as linear, constant, identity, square or quadratic, cubic, square root, reciprocal,  absolute value       and greatest integer function

18.     sketch the graph of a piecewise defined function and confirm on the graphing calculator

19.     analyze the effect of and determine vertical and horizontal shifts, stretches and shrinks, and reflections about the axes of a basic graph

20.     find the equation for the sum, difference, product, or quotient of two  given functions and determine the domain of each

21.     find the composite of two given functions and determine the domain of the composite

22.     find two functions, f and g, such that  for a given function h

23.     find the inverse and its domain and range of a given one to one function and verify that two functions f(x) and g(x) are inverses of each other by showing f(g(x)) = x  and g(f(x)) = x

24.     determine whether a given set of ordered pairs, given graph, or given equation is a one to one function

25.     graph a function and its inverse on the same axes and graph the line of symmetry y = x

26.     use mathematical models to analyze sets of data

27.     write mathematical models for direct variation, inverse variation, and joint variation

28.     use the regression function of a graphing calculator to find the equation of a least squares regression line

29.     solve applications/word problems which assess all of the above topics


1.        polynomial function and its degree

2.        parabola

3.        vertex (h,k) of a parabola

4.        standard form of a quadratic function

5.        continuity of a polynomial function

6.        zeros, roots or solutions of a polynomial and their multiplicity k

7.        Intermediate Value Theorem

8.        Remainder Theorem

9.        Factor Theorem

10.     complex numbers

11.     Fundamental Theorem of Algebra

12.     Linear Factorization Theorem

13.     Rational Zeros Test

14.     Descartes Rule of Signs

15.     upper and lower bounds on real zeros

16.     rational functions

17.     discontinuity of a rational function

18.     vertical asymptotes

19.     horizontal asymptotes

20.     slant or oblique asymptotes

21.     synthetic division

1.        sketch the graph of a polynomial or rational function and confirm the sketch by choosing an appropriate viewing window on the graphing calculator

2.        put a quadratic function in standard form to identify the vertex, and  intercepts to aid in graphing it

3.        identify the vertex of a parabola from its graph and write its equation in standard form

4.        use transformations to assist in sketching the graph of a given polynomial function

5.        determine the left and right end behavior of a polynomial using the degree and leading coefficient

6.        find all real zeros of a polynomial or rational function and their multiplicity and confirm the zeros by using the “root” or “zero” function on the graphing calculator

7.        describe the behavior of the graph of a polynomial at a zero with an odd or even multiplicity

8.        write an equation of a polynomial having given zeros and a given degree

9.        perform algebraic long division and synthetic division of polynomials

10.     evaluate a polynomial by using the remainder theorem and synthetic division

11.     find, if possible, all the zeros and their multiplicity of a polynomial function with real coefficients and write the polynomial as a product of linear and irreducible quadratic factors over the real numbers using the Rational Zeros Theorem and upper and lower bounds on the zeros

12.     determine if two complex numbers are equal

13.     add, subtract, and multiply complex numbers

14.     use complex conjugates to write the quotient of two complex numbers in standard form

15.     find complex solutions of quadratic equations

16.     use Descartes Rule of Signs to determine the possible number of positive and negative zeros a polynomial has

17.     find the upper and lower bounds on the real zeros for a given polynomial

18.     find the domain, range, vertical, horizontal, and/or oblique asymptotes, if any, for a given rational function

19.     solve applications that result in equations which are polynomial or rational functions




1.        algebraic functions

2.        transcendental functions

3.        exponential function with base b or e

4.        continuously compounded interest and interest compounded n times annually

5.        logarithmic functions with base a, base 10, or base e

6.        common logarithms

7.        natural logarithms

8.        change of base formula

9.        properties of logarithms

1.        graph a given exponential function or logarithmic function, indicate its domain and range, x or y intercept, describe it as increasing or decreasing and identify any asymptotes the graph has

2.        perform vertical and horizontal shifts, stretches and shrinks and reflections when given an exponential or logarithmic function together with its graph

3.        convert a given equation from exponential to equivalent log form or from log to equivalent exponential form

4.        simplify and evaluate log expressions

5.        write a given expression as a single log using the properties of logarithms

6.        use the change of base formula to find the log of any number in any base > 0 using base 10 or base e

7.        Solve applications that result in exponential or log equations such as radioactive decay, bacterial growth, compound interest, decibel level, earthquake intensity, etc.

8.        solve exponential equations by converting to log form or by converting to the same base and equating  exponents

9.        solve log equations by converting to exponential form or by using the properties of logs

10.     use a graphing calculator to solve exponential and log equations

11.     recognize exponential growth, exponential decay, Gaussian, logistic growth, and logarithmic models and use these models to solve given problems                                                                                               


1.        system of 2 linear equations in 2 variables

2.        solution of a system of equations

3.        points of intersection and graphing method of solution

4.        substitution method of solution

5.        break-even point

6.        elimination by addition or subtraction method

7.        equivalent systems

8.        consistent systems

9.        inconsistent systems

10.     independent systems

11.     dependent systems

12.     row-echelon form

13.     ordered triple

14.     Gaussian elimination method

15.     nonsquare systems of equations

16.     linear inequalities

17.     solution of an inequality

18.     graph of an inequality

19.     solution of a system of inequalities

20.     linear programming

21.     optimization

22.     objective function

23.     constraints

24.     feasible solutions

25.     optimal feasible solution

1.        Solve a system of 2 equations in 2 variables by graphing and finding the points of intersection, if any.  If a special case results (same line or parallel lines or no intersection) you should be able to identify the system as dependent or inconsistent or having no solution respectively.

2.        solve a system by substitution which works best if at least one equation has one variable with a coefficient of  + 1

3.        solve a system by addition or subtraction to eliminate one of the variables

4.        use back substitution to solve linear systems in row-echelon form

5.        use Gaussian elimination to solve systems of linear equations

6.        solve nonsquare systems of linear equations and write the solution as an ordered triple in terms of  an independent variable

7.        sketch the graphs of inequalities in 2 variables and shade the solution region

8.        solve systems of inequalities and shade the solution region for the system and describe the solution as bounded or unbounded

9.        solve a linear programming problem by identifying the objective function or the quantity to be optimized, setting up a system of linear constraints or inequalities, graphing their intersection to determine the vertices of the set of feasible solutions and substituting these vertex points in the objective function to see which gives the optimal value

10.     solve applications that result in systems of equations or inequalities or linear programming  problems and use a graphing calculator where possible to aid in each of these topics



1.        matrix

2.        order of a matrix (m x n)

3.        square matrix

4.        column matrix

5.        row matrix

6.        entry of a matrix notation (aij)

7.        augmented matrix

8.        coefficient matrix

9.        row equivalent matrices

10.     principal or main diagonal of a matrix

11.     elementary row operations

12.     row-echelon form

13.     reduced row echelon form

14.     Gauss-Jordan elimination method

15.     determinant of a square matrix

16.     minors

17.     cofactors

18.     Cramer’s Rule

1.        write a matrix and identify its order

2.        perform elementary row operations on matrices

3.        use the augmented matrix for a system and the Gaussian elimination or the Gauss Jordan elimination method to solve a system of linear equations

4.        describe an entry in a matrix using aij notation

5.        find the determinant of a 2x2 matrix

6.        find minors and cofactors of square matrices

7.        find determinants of an n x n square matrix

8.        use Cramer’s Rule to solve a system of linear equations

9.        solve applications that result in systems of equations