is
a function of 
”;
identify as
the input and as
the output.TRI-COUNTY TECHNICAL COLLEGE
COURSE SYLLABUS
Course Prefix & Number: MAT 109
Course Title: College Algebra with Modeling
Class Hours Lab Hours Credits
Per week: 3 Per Week: 0 Awarded: 3
Catalog Description: This course is an approach to algebra that incorporates mathematical modeling of real data and business applications. Emphasis on linear, quadratic, piece-wise defined, rational, polynomial, exponential and logarithmic functions. Includes inequalities and matrices.
Entry Level Skills: Elementary and intermediate algebra facts and techniques
Pre-requisites: Satisfactory score on mathematics placement exam or MAT 102 with a grade of C or better
Co-requisites: None
Text(s)/Required Materials: Functions Modeling Change, by Connally, Hughes-Hallett, Gleason, et al., 3rd Edition, John Wiley & Sons, Inc, 2007.
Equipment: Graphing calculator (TI-83 Plus or TI-84 Plus recommended). CAS calculators (TI-89, TI-92, Voyage 200) are not permitted in this course.
Course Competencies and Objectives/ Major Course Topics:
Unit 1: Functions, Lines, and Change
Upon completion of this unit (Sections 1.1-1.5) the student should be able to:
1.
Recognize and translate the verbal phrase “ is
a function of ”;
identify as
the input and as
the output.
2. Determine if one variable is a function of the other for relationships expressed numerically, graphically, verbally, and symbolically.
3. Calculate the average rate of change on a given interval using values from a graph, a table, a formula, or a written problem.
4. Describe a function as increasing or decreasing on a given interval, and recognize the connection to the sign of the average rate of change.
5. Identify a linear function by recognizing a constant rate of change given a function in any form, and then determine the equation of the linear function.
6.
Interpret the slope using steepness and rate of change; interpret a
linear formula using initial value 
and
rate of increase or decrease 
.
7.
Recognize how changes in the parameters
and
affect
the graph of a linear function.
8. Calculate the intersection of two or more lines algebraically and graphically.
9. Determine equations of horizontal and vertical lines, and recognize the slope of each.
10. Recognize parallel and perpendicular lines through their slopes.
Unit 2: Functions, Quadratics, and Concavity
Upon completion of this unit (Sections 2.1 –2.6) the student should be able to:
1. Identify and calculate input and output values given any representation of a function.
2. Find the domain and range of a function in any form, thinking in terms of inputs and outputs.
3. Graph a piecewise defined function; write a formula for a piecewise function given a verbal description.
4. Find the composition of a function algebraically, and give the meaning.
5. Find the inverse for a function that is defined by a formula.
6. Recognize concavity of functions given in any representation.
7. Relate the concavity of a function to whether the rate of change increases or decreases.
8.
Calculate zeros of a quadratic function by factoring and by using the
quadratic formula, and relate the zeros to the
-intercepts
of the graph.
9. Recognize the type of concavity for a quadratic function and relate the concavity of the curve to the rate of change.
Unit 3: Exponential and Logarithmic Functions
Upon completion of this unit (Sections 3.1 – 3.5 and 4.1 – 4.3) the student should be able to:
1. Recognize an exponential function as having a constant percent growth rate.
2. Recognize and use increasing exponential functions to model growth, and decreasing exponential functions to model decay for functions in any form.
3. Use percent growth rates to determine annual growth factors, and vice versa.
4. Write equations for exponential functions in general form, and algebraically solve for any of the parameters.
5. Compare linear and exponential models when given a table of values, determine which function is linear and which is exponential, and find formulas for either.
6. Analyze the effect of the parameters on the exponential family of graphs.
7. Use the horizontal asymptote to describe end behavior of an exponential function.
8. Solve exponential equations graphically.
9.
Convert exponential functions between the forms
and
.
10.
Recognize the continuous growth rate
,
and differentiate among exponential graphs with differing growth rates.
11. Solve compound interest problems involving both discrete and continuous compounding.
12. Convert statements between exponential and logarithmic form.
13. Know the properties of common and natural logarithms and use them to algebraically solve exponential equations.
14. Solve applications involving doubling time and half-life for both the general and continuous forms of exponential functions.
15. Analyze logarithmic graphs, including domain and range, intercepts, and vertical asymptote.
16. Solve problems involving real world applications of logarithms such as chemical acidity and sound intensity.
Unit 4: Transformations, Compositions, and Inverses of Functions
Upon completion of this unit (Sections 5.1 – 5.5 and 8.1 – 8.2) the student should be able to:
1. Recognize the general form for translations (vertical and horizontal shifts, reflections, vertical and horizontal stretches and compressions) and how they affect a function in terms of its graph and formula.
2. Use symmetry to identify even and odd functions in any form.
3. Recognize a combination of translations and use them to transform a function in any form.
4. Analyze a quadratic function through transformations, recognizing its axis of symmetry, vertex, zeros, and whether the parabola opens up or down.
5. Write quadratic functions in either standard form or vertex form.
6. Find a formula for a quadratic function given information about the graph.
7. Solve applications involving quadratic functions.
8. Find the composition of functions given any representation.
9. Decompose functions by working backwards to find the functions that went into a composition.
10. Find a formula for an inverse function.
11. Use the horizontal line test to determine if a function is invertible.
12.
Recognize that the graphs of a function and its inverse are symmetric
about the line 
.
13.
Recognize that the domain and range of
are
obtained by interchanging the domain and range of
.
Unit 5: Polynomial and Rational Functions; Matrices
Upon completion of this unit (Sections 9.1 – 9.5 and 10.5) the student should be able to:
1. Write formulas for direct and inverse proportions, given verbal descriptions (including applications).
2.
Recognize the effect of the value of the power
on
graphs of power functions.
3. Find the formula for a power function from two points on its graph (including applications).
4. Recognize polynomial functions, write polynomials in standard form, and identify the leading term and use it to identify long-run behavior of a polynomial.
5. Rewrite a polynomial function as a product of linear factors, find the zeros, and use the zeros to describe the short-run behavior.
6. Solve a polynomial inequality by recognizing within the graph where the function is positive or negative.
7.
Recognize how repeated zeros affect how the graph intercepts the
-axis.
8. Write a formula for a polynomial function when given its graph.
9. Describe the long-run behavior of a given rational function; find the horizontal asymptote, if it exists.
10. Determine zeros and vertical asymptotes of a rational function.
11. Graph rational functions, including intercepts and asymptotes.
12. Express a table of numbers in matrix form, and manipulate matrices through addition, subtraction, and scalar multiplication.
Grade Calculation Method: The exact method of calculating your grade will be distributed by your instructor at the beginning of the course, based on these guidelines:
Unit Tests = 70-85%
Other (Homework, Projects, etc) = 0-15%
Cumulative Final Exam = 15-20%
TOTAL 100%
Prepared by: Robin Pepper Date written or revised: May 14, 2007