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Effective: Summer 2014
MATH 48BPRECALCULUS II5 Unit(s)

Prerequisites: Prerequisite: MATH 48A.
Advisory: Advisory: Demonstrated proficiency in English by placement as determined by score on the English placement test OR through an equivalent placement process OR completion of ESLL 25 & ESLL 249; UC credit for MATH 48A, B & C is limited to a maximum of 7.5 units for the combination or any portion of the series completed.
Grade Type: Letter Grade, the student may select Pass/No Pass
Not Repeatable.
FHGE: Communication & Analytical Thinking Transferable: CSU/UC
5 hours lecture. (60 hours total per quarter)

Student Learning Outcomes -
  • A successful student will be able to graph, analyze and transform rational, exponential and logarithmic functions.
  • A successful student will be able to model real-life phenomenon using rational, trigonometric, exponential and logarithmic functions, use the model to make predictions, and interpret solutions within the context of the real-life phenomenon.
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:
  1. Graph and analyze rational functions and solve related equations and inequalities
  2. Graph and analyze exponential functions and solve related equations and inequalities
  3. Graph and analyze logarithmic functions and solve related equations and inequalities
  4. Analyze combinations of functions
  5. Analyze piecewise functions
  6. Investigate composition of functions
  7. Model data with linear, quadratic, power, exponential, logarithmic, polynomial and rational functions
  8. 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.
  9. Discuss mathematical problems and write solutions in accurate mathematical language and notation
  10. Interpret mathematical solutions
Special Facilities and/or Equipment -
  1. Graphing Calculator
  2. When taught hybrid: Four lecture hours per week in face-to-face contact and one hour per week using CCC Confer. Students need internet access.

Course Content (Body of knowledge) -
  1. Graph and analyze rational functions and solve related equations and inequalities
    1. Examine vertical, horizontal asymptotes and removable discontinuities
    2. Find limits of and at infinity
    3. Find the domain of rational functions
    4. Graph functions that contain vertical and horizontal asymptotes
    5. Solve equations and inequalities involving rational expressions
    6. Investigate applications involving rational functions
    7. Interpret the meaning of asymptotes in real-world applications
    8. Find the inverse of a rational function
  2. Graph and analyze exponential functions and solve related equations and inequalities
    1. Calculate change factors from tables and graphs
    2. Calculate percentage rates of change from tables, graphs and change factors
    3. Recognize the difference between functions with a constant percentage change and functions with a constant difference change
    4. Construct exponential models algebraically from tables or words
    5. Use exponential models to predict and interpret results
    6. Graph exponential functions given in equations, tables or words
    7. Use exponential regression to model real-world data sets
    8. Examine applications involving half-life and double time
    9. Investigate the relationship between growth factors and graphs of exponential functions
    10. Investigate exponential growth and decay problems
    11. Investigate the number e
    12. Solve equations and inequalities involving exponential functions
    13. Investigate applications involving exponential functions such as:
      1. Compound interest
      2. Exponential population models
      3. Radioactive decay
      4. Newton's law of cooling
    14. Find the inverse of an exponential function
  3. Graph and analyze logarithmic functions and solve related equations and inequalities
    1. Graph logarithmic and exponential functions from equations and tables
    2. State and use properties of logarithms
    3. Identify common and natural logarithms
    4. Solve exponential equations using logarithms and interpret the real-world meaning of the results
    5. Solve logarithmic equations and interpret the real-world meaning of the results
    6. Investigate applications involving logarithms such as:
      1. pH
      2. Intensity of sound
      3. Intensity of earthquakes
    7. Use logarithmic regression to model real-world data sets
    8. Use logarithms to linearize exponential data to find an exponential model
  4. Analyze combinations of functions
    1. Compute the sum, difference, product, or quotient of functions
    2. Use combination of functions to model real-world situations
    3. Determine the practical and theoretical domain and range of the combination of functions
  5. Analyze piecewise functions
    1. Define piecewise functions using equations, tables, graphs and words
    2. Determine function values of piecewise functions from a graph, equation, and table
    3. Construct piecewise functions to model real-world situations
    4. Investigate absolute value functions
      1. Solve inequalities involving absolute values
  6. Investigate composition of functions
    1. Compose two or more functions using tables, equations, or graphs
    2. Create, use and interpret function composition
  7. Model data with linear, quadratic, power, exponential, logarithmic, polynomial and rational functions
    1. Select the best function to model a real-world data set given a graph, table of data or verbal description
    2. Use the appropriate function to predict and interpret unknown results
  8. 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
    1. Calculator/computer utilities for evaluating problems involving optimization
    2. Calculator/computer utilities for determining mathematical models using regression
    3. Calculator/computer utilities for finding intersection points for graphs of two functions
    4. Calculator/computer utilities for finding zeros or roots of functions
  9. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
    1. Application problems from other disciplines
    2. Proper notation
  10. Interpret mathematical solutions.
    1. Explain the significance of solutions to application problems.
Methods of Evaluation -
  1. Homework
  2. Quizzes
  3. Exams
  4. Proctored Comprehensive Final Exam
  5. Class Participation
  6. Exploratory worksheets or labs
  7. 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 -
  1. Lecture
  2. Discussion
  3. Cooperative learning exercises
 
Lab Content -
Not applicable.
 
Types and/or Examples of Required Reading, Writing and Outside of Class Assignments -
  1. 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.
  2. 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.
  3. 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.
  4. 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.