  
Student Learning Outcomes 
 Students will model, solve, and interpret applications using rational, exponential, logarithmic, absolute value, composite, and piecewisedefined functions.
 Students will develop conceptual understanding of rational, exponential, logarithmic, absolute value, composite, and piecewisedefined functions. They will demonstrate and communicate this understanding by graphing, analyzing, and transforming these functions and connecting their multiple representations.
 Students will solve rational, exponential, and logarithmic equations.

Description  
 This course is a continuation of topics from MATH 48A. Topics include rational, exponential and logarithmic functions, piecewise functions, combination and composition of functions and an introduction to trigonometry.


Course Objectives  
 The student will be able to:
 Graph and analyze rational functions and solve related equations and inequalities
 Graph and analyze exponential functions and solve related equations and inequalities
 Graph and analyze logarithmic functions and solve related equations and inequalities
 Analyze combinations of functions
 Analyze piecewise functions
 Investigate composition of functions
 Model data with linear, quadratic, power, exponential, logarithmic, polynomial and rational functions
 Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (G) above.
 Discuss mathematical problems and write solutions in accurate mathematical language and notation
 Interpret mathematical solutions

Special Facilities and/or Equipment  
  Graphing Calculator
 When taught hybrid: Four lecture hours per week in facetoface contact and one hour per week using CCC Confer. Students need internet access.

Course Content (Body of knowledge)  
  Graph and analyze rational functions and solve related equations and inequalities
 Examine vertical, horizontal asymptotes and removable discontinuities
 Find limits of and at infinity
 Find the domain of rational functions
 Graph functions that contain vertical and horizontal asymptotes
 Solve equations and inequalities involving rational expressions
 Investigate applications involving rational functions
 Interpret the meaning of asymptotes in realworld applications
 Find the inverse of a rational function
 Graph and analyze exponential functions and solve related equations and inequalities
 Calculate change factors from tables and graphs
 Calculate percentage rates of change from tables, graphs and change factors
 Recognize the difference between functions with a constant percentage change and functions with a constant difference change
 Construct exponential models algebraically from tables or words
 Use exponential models to predict and interpret results
 Graph exponential functions given in equations, tables or words
 Use exponential regression to model realworld data sets
 Examine applications involving halflife and double time
 Investigate the relationship between growth factors and graphs of exponential functions
 Investigate exponential growth and decay problems
 Investigate the number e
 Solve equations and inequalities involving exponential functions
 Investigate applications involving exponential functions such as:
 Compound interest
 Exponential population models
 Radioactive decay
 Newton's law of cooling
 Find the inverse of an exponential function
 Graph and analyze logarithmic functions and solve related equations and inequalities
 Graph logarithmic and exponential functions from equations and tables
 State and use properties of logarithms
 Identify common and natural logarithms
 Solve exponential equations using logarithms and interpret the realworld meaning of the results
 Solve logarithmic equations and interpret the realworld meaning of the results
 Investigate applications involving logarithms such as:
 pH
 Intensity of sound
 Intensity of earthquakes
 Use logarithmic regression to model realworld data sets
 Use logarithms to linearize exponential data to find an exponential model
 Analyze combinations of functions
 Compute the sum, difference, product, or quotient of functions
 Use combination of functions to model realworld situations
 Determine the practical and theoretical domain and range of the combination of functions
 Analyze piecewise functions
 Define piecewise functions using equations, tables, graphs and words
 Determine function values of piecewise functions from a graph, equation, and table
 Construct piecewise functions to model realworld situations
 Investigate absolute value functions
 Solve inequalities involving absolute values
 Investigate composition of functions
 Compose two or more functions using tables, equations, or graphs
 Create, use and interpret function composition
 Model data with linear, quadratic, power, exponential, logarithmic, polynomial and rational functions
 Select the best function to model a realworld data set given a graph, table of data or verbal description
 Use the appropriate function to predict and interpret unknown results
 Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (G) above
 Calculator/computer utilities for evaluating problems involving optimization
 Calculator/computer utilities for determining mathematical models using regression
 Calculator/computer utilities for finding intersection points for graphs of two functions
 Calculator/computer utilities for finding zeros or roots of functions
 Discuss mathematical problems and write solutions in accurate mathematical language and notation.
 Application problems from other disciplines
 Proper notation
 Interpret mathematical solutions.
 Explain the significance of solutions to application problems.

Methods of Evaluation  
  Homework
 Quizzes
 Exams
 Proctored Comprehensive Final Exam
 Class Participation
 Exploratory worksheets or labs
 Group projects

Representative Text(s)  
 Wilson, Adamson, Cox and O'Bryan, Precalculus: A Make It Real Approach, 1st Edition, Cengage Learning, 2013. Stewart, Redlin, and Watson, Precalculus: Mathematics for Calculus, 6th Edition, Cengage Learning, 2012.

Disciplines  
 Mathematics


Method of Instruction  
  Lecture
 Discussion
 Cooperative learning exercises


Lab Content  
 Not applicable.


Types and/or Examples of Required Reading, Writing and Outside of Class Assignments  
  Homework Problems: Homework problems covering subject matter from text and related material ranging from 30  60 problems per week. Students will need to employ critical thinking in order to complete assignments.
 Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.
 Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system such as Mathematica or MATLAB.
 Worksheets: Problems and activities covering the subject matter.
Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class.
