  
Student Learning Outcomes 
 A successful student will be able to graph, analyze and transform polynomial, power, and root functions.
 A successful student will be able to model reallife phenomenon using polynomial, power & root functions, use the model to make predictions, and interpret solutions within the context of the reallife phenomenon

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.


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