Course Outline for Mathematics 21
College Algebra for BSTEM
Effective: Fall 2022
SLO Rev: 09/13/2021
SLO Rev: 09/13/2021
Catalog Description:
MTH 21 - College Algebra for BSTEM
5.00 Units
College level course in algebra for majors in Business and STEM fields (BSTEM). Concepts covered include polynomial, rational, radical, exponential, piecewise, and logarithmic functions and their graphs; nonlinear systems of equations and inequalities; theory of polynomial equations; and sequences and series.
Prerequisite: MTH 55 or an appropriate skill level demonstrated through the Mathematics Assessment Process. May not receive credit if MTH 31 has been completed.
1701.00 - Mathematics, General
Letter Grade Only
| Type | Units | Inside of Class Hours | Outside of Class Hours | Total Student Learning Hours |
|---|---|---|---|---|
| Lecture | 5.00 | 90.00 | 180.00 | 270.00 |
| Total | 5.00 | 90.00 | 180.00 | 270.00 |
Measurable Objectives:
Upon completion of this course, the student should be able to:
- analyze and investigate properties of functions;
- apply transformations to the graphs of functions;
- recognize the relationship between functions and their inverses graphically and algebraically;
- solve and apply rational, linear, polynomial, radical, absolute value, exponential, and logarithmic equations;
- solve and apply nonlinear, and rational inequalities;
- solve systems of equations and inequalities;
- apply techniques for finding zeros of polynomials and roots of equations;
- apply functions and other algebraic techniques to model real world applications;
- use formulas to find sums of finite and infinite series.
Course Content:
- Functions, relations, and their graphs
- Algebraic functions, including polynomial and rational functions
- Algebraic relations
- Domain and Range of a function
- Using the function
- Using the graph
- Graphing functions
- Absolute value functions
- Rational functions
- Radical functions
- Exponential functions
- Logarithmic functions
- Polynomial functions of degree 3 or higher
- Characteristics of graphs
- Relationship between the algebraic transformation of a function and the geometric transformation of its graph
- Intercepts
- Solve for intercepts
- Local behavior of polynomial x-intercepts
- Discontinuities
- Holes
- Vertical asymptotes
- local behavior
- End Behavior
- Horizontal asymptotes
- End behavior of functions
- Increasing and decreasing
- Even and odd functions and their symmetry
- Function arithmetic
- Composite and inverse functions
- Invertibility
- Using a graph
- Using algebraic methods
- Relationship of domain and range of a function and the domain and range of its inverse
- Compare the graphs of a function and its inverse
- Using domain restrictions to create a one-to-one function
- Define function that is part of a circle/parabola and find its inverse
- Piecewise functions
- Definition
- Graphing with restricted domains
- Absolute value defined as a piecewise function
- Modeling and applications
- Difference quotient and limit
- Objective function
- Arithmetic of complex numbers
- Roots of polynomial equations
- Polynomial division
- Fundamental theorem of algebra
- Remainder theorem
- Rational roots theorem
- Conjugate complex roots
- Exponential and logarithmic equations and functions
- Properties of logarithms
- Exponential and logarithmic equations
- Graph exponential and logarithmic functions using transformations
- Domain and range
- Applications of exponential growth and decay
- System of equations
- Linear systems of three or more variables
- Substitution method
- Elimination method
- Gauss-Jordan reduction of extended matrix
- Nonlinear systems
- Nonlinear polynomial and rational inequalities
- Algebraic methods
- Graphical methods
- Sequences and series
- Summation notation
- Summations algebra
- Arithmetic and geometric series
- The Binomial Theorem
- Additional algebraic techniques
- Factoring using substitution
- Simplifying expressions
- Partial fractions
Methods of Instruction:
- Lectures
- Class and group discussions
- Hands-on Activities
- Distance Education
Assignments and Methods of Evaluating Student Progress:
- Determine the equation of a function whose graph is the graph of y=log(x) stretched by a factor of 2, reflected over the x-axis, and translated 3 units to the left and 1 unit up.
- Consider a rectangle in Quadrant 1 that is bounded by the x- and y-axis and has a corner on the graph of y=20-x^2. Find the dimensions of such a rectangle if its area is 16 square units.
- The population of a certain city was 112,000 in 1994, and the observed relative growth rate is 4% per year. Find a function that models the population after t years. In what year will the population reach 200,000?
- Exams/Tests
- Final Examination
- Quizzes
- Homework
Upon the completion of this course, the student should be able to:
- Critically analyze mathematical problems using a logical methodology.
- Communicate mathematical ideas, understand definitions, and interpret concepts.
- Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
- Blitzer, R. (2022). College Algebra (7). Pearson.
Abbreviated Class Schedule Description:
In this course students continue to build the algebric skills necessary for success in future Business/STEM math courses. Concepts covered include polynomial, rational, radical, exponential, piecewise, and logarithmic functions and their graphs; nonlinear systems of equations and inequalities; theory of polynomial equations; and sequences and series.
Prerequisite: MTH 55 or an appropriate skill level demonstrated through the Mathematics Assessment Process. May not receive credit if MTH 31 has been completed.
Discipline:
Mathematics*