Foothill CollegeApproved Course Outlines

Physical Sciences, Mathematics & Engineering Division
MATH 48APRECALCULUS ISummer 2014
5 hours lecture.5 Units

Total Quarter Learning Hours: 60 (Total of All Lecture, Lecture/Lab, and Lab hours X 12)
 
 Lecture Hours: 5 Lab Hours: Lecture/Lab:
 Note: If Lab hours are specified, see item 10. Lab Content below.

Repeatability -
Statement: Not Repeatable.

Status -
 Course Status: ActiveGrading: Letter Grade with P/NP option
 Degree Status: ApplicableCredit Status: Credit
 Degree or Certificate Requirement: AS Degree,   Foothill GE
 GE Status: Communication & Analytical Thinking

Articulation Office Information -
 Transferability: BothValidation: 6/10; 11/27/12;11/16/13

1. Description -
Introduction to functions and families of functions including quadratics, polynomials, power and root functions, transformations of these functions, and their use in solving applications problems.
Prerequisite: Satisfactory score on the mathematics placement test or MATH 105 or 108.
Co-requisite: None
Advisory: Demonstrated proficiency in English by placement into ENGL 1A as determined by score on the English placement test or through an equivalent placement process; 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.

2. Course Objectives -
The student will be able to:
  1. Examine the definition of a function and investigate the different forms of a function.
  2. Understand and compute rates of change.
  3. Compute a regression model and use it to make predictions.
  4. Explore transformations of functions.
  5. Investigate quadratic functions.
  6. Explore higher-order polynomial functions.
  7. Investigate power functions and relationship between direct and inverse variation.
  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.
3. 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.

4. Course Content (Body of knowledge) -
  1. Examine the definition of a function and investigate the different forms of a function.
    1. Define a function
      1. Determine a relation vs. a function
      2. Explain how a function is a process or a correspondence
      3. Write and interpret functions using function notation
    2. Explore symbolic, numeric, graphical and verbal forms of a function.
      1. Determine if a graph or table of data represents a function
      2. Be able to convert words representing function relationships into symbolic and graphical representations
      3. Translate functions given in equations, tables and graphs into words
      4. Solve function equations and system of equations for a given variable using an equation, table, and graph
      5. Create and use basic function formulas to model real-word situations
    3. Determine and interpret the domain and range of a function
      1. Be able to find the practical domain and range of a function when applied to a real-life situation
    4. Determine and interpret the horizontal and vertical intercepts of a function
    5. Graph functions on the rectangular coordinate system
    6. Inverse functions
      1. Explain the relationship between a function and its inverse
      2. Understand and be able to determine one-to-one functions
      3. Explore the relationship between the graph of a function and its inverse
      4. Investigate the relationship between the domain and range of a function and its inverse
      5. Explain and use inverse function notation to solve real-world problems
      6. Find the inverse of a function from a table, graph or equation
      7. Interpret the practical meaning of an inverse function when applied to a real-life situation
  2. Understand and compute rates of change.
    1. Calculate average rate of change from a table, graph and an equation
    2. Understand the implications of a function that has a constant rate of change
    3. Understand the implications of a function that has a variable rate of change
    4. Determine if a function is increasing and decreasing from a table or a graph
    5. Determine the concavity of a function from a table or graph
    6. Interpret the meaning of an average rate of change in the context of a situation
  3. Compute a regression model and use it to make predictions.
    1. Use linear regression to find the equation of the line of best fit
    2. Use a linear regression model to make predictions
    3. Use quadratic regression to find a quadratic function of best fit
    4. Use cubic regression to find a cubic function of best fit
    5. Understand the usage of the correlation coefficient and the coefficient of determination
  4. Explore transformations of functions.
    1. Identify and graph the change in a function that results in a vertical or horizontal shift
    2. Identify and graph the change in a function that results in a horizontal or vertical reflection
    3. Identify and graph the change in a function that results in a vertical stretch or compression
    4. Identify and graph the change in a function that results in a horizontal stretch or compression
    5. Be able to recognize the change in a graph of a function when a combination of transformations is applied
    6. Understand the impact a transformation has on the average rate of change of a function
    7. Understand the concept of symmetry of functions
    8. Be able to determine if a function is even, odd, or neither
  5. Investigate quadratic functions
    1. Recognize the relationship between a quadratic equation and its graph
    2. Construct and use quadratic models to predict results and interpret the findings in a real-world context
    3. Express quadratic functions in vertex, standard, and factored form
    4. Determine vertex, horizontal and vertical intercepts of a quadratic function from an equation, data table or formula
    5. Identify relative maxima and minima as vertices
    6. Use the quadratic formula to solve real-world problems
    7. Solve quadratic inequalities and perform sign analysis
    8. Investigate applications such as:
      1. Projectile motion
      2. Free fall
      3. Area
      4. Quadratic economic models
  6. Explore higher-order polynomial functions
    1. Understand the definition of a polynomial function
    2. Explore the end behavior of graphs of polynomial functions
    3. Explore the graphs of polynomial functions using the relationship between zeros and factors
    4. Identify relative extrema of polynomial functions
    5. Investigate the Fundamental Theorem of Algebra
      1. Identify zeros of a polynomial including complex zeros
    6. Solve inequalities involving higher-order polynomials
    7. Investigate applications of higher-order polynomial functions
  7. Investigate power functions and relationship between direct and inverse variation.
    1. Draw and recognize graphs of
      1. Power functions y = f(x) = a*x^b, where b is any real-number value
      2. Root functions y=f(x)=x^(1/n), where n is an positive integer
    2. Investigate applications involving direct and inverse variation, such as
      1. Hooke's law
      2. Intensity of illumination or radio waves
      3. Length and period of a pendulum
      4. Gravitational force
      5. Distance, constant velocity, and time
  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.
5. Repeatability - Moved to header area.
 
6. 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
7. 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.

8. Disciplines -
Mathematics
 
9. Method of Instruction -
  1. Lecture
  2. Discussion
  3. Cooperative learning exercises
 
10. Lab Content -
Not applicable.
 
11. Honors Description - No longer used. Integrated into main description section.
 
12. 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.
13. Need/Justification -
This course is a required core course for the AS degree in General Studies Science, a restricted support course for the Certificate of Achievement in Transfer Studies: CSU GE and satisfies the Foothill GE Requirement for Area V, Communication and Analytical Thinking.


Course status: Active
Last updated: 2014-03-21 20:26:51


Foothill CollegeApproved Course Outlines