PreCalculus B: Functions & Graphical Analysis

Course Description:

This course is the second in a two-course sequence that broadens student understanding of functions and mathematical models of real-world phenomena. Designed to prepare a student for Calculus, this course will build on student understanding of algebra, extending their knowledge to new mathematical topics, while deepening their knowledge in others. The course contains units on polynomial, rational, logarithmic and exponential functions, sequences, series, conics and limits, as well as systems and vectors. The majority of the course is asynchronous with a few synchronous elements.

Course Details:

Course Title (District): PreCalculus B: Functions & Graphical Analysis
Course Title (NCES SCED) : Pre-Calculus
Course Provider : Whitehall District Schools
Content Provided By : Michigan Virtual
Online Instructor Provided By : Whitehall District Schools
Standards Addressed : MMC, NCAA
Ailgnment Document :
Academic Terms : Accelerated, Semester, Trimester
Subject Area : Mathematics
Course Identifier : Pre-Calculus
Course Level : (G) General or Regular
Available Credit : 0.5
Sequence : 2 of 2

How To Enroll:

Enrollment Website :
Email : [email protected]
Phone : (888) 889-2840

Students and Parents: It is important to work closely with your local school counselor or registrar to follow the school's enrollment procedures. By clicking the "Start Registration Request" button below, you will be able to notify the school of your interest in registering for the online course. However, it is the responsibility of the district or school to review the registration request and approve or deny the request. Please make a note to follow up with your school after submitting a registration request.

Start Registration Request

Additional Course Information:

Upon completion of this course, students will be able to…

  • Perform algebraic operations (including compositions) on functions and apply transformations.
  • Write an expression for the composition of one given function with another and find the domain, range, and graph of the composite function. Recognize components when a function is composed of two or more elementary functions.
  • Identify and describe discontinuities of a function and how these relate to the graph.
  • Use the idea of limit to analyze a graph as it approaches an asymptote. Compute limits of simple functions informally.
  • Use the inverse relationship between exponential and logarithmic functions to solve equations and problems.
  • Graph logarithmic functions. Graph translations and reflections of these functions.
  • Compare the large-scale behavior of exponential and logarithmic functions with different bases and recognize that different growth rates are visible in the graphs of the functions.
  • Solve exponential and logarithmic equations when possible. For those that cannot be solved analytically, use graphical methods to find approximate solutions.
  • Explain how the parameters of an exponential or logarithmic model relate to the data set or situation being modeled. Find an exponential or logarithmic function to model a given data set or situation. Solve problems involving exponential growth and decay.
  • Solve quadratic-type equations by substitution.
  • Apply quadratic functions and their graphs in the context of motion under gravity and simple
    optimization problems.
  • Explain how the parameters of an exponential or logarithmic model relate to the data set or situation being modeled. Find a quadratic function to model a given data set or situation.
  • Solve polynomial equations and inequalities of degree greater than or equal to three. Graph polynomial functions given in factored form using zeros and their multiplicities, testing the sign-on intervals and analyzing the function’s large-scale behavior.
  • Recognize and apply fundamental facts about polynomials: the Remainder Theorem, the Factor Theorem, and the Fundamental Theorem of Algebra.
  • Solve equations and inequalities involving rational functions. Graph rational functions given in factored form using zeros, identifying asymptotes, analyzing their behavior for large x values, and testing intervals.
  • Given vertical and horizontal asymptotes, find an expression for a rational function with these features.
  • Recognize and apply the definition and geometric interpretation of difference quotient. Simplify difference quotients and interpret difference quotients as rates of change and slopes of secant lines.
  • Perform operations (addition, subtraction, and multiplication by scalars) on vectors in the plane.
  • Solve applied problems using vectors.
  • Recognize and apply the algebraic and geometric definitions of the dot product of vectors.
  • Define matrix addition and multiplication. Add, subtract, and multiply matrices.
  • Multiply a vector by a matrix.
  • Represent rotations of the plane as matrices and apply to find the equations of rotated conics.
  • Define the inverse of a matrix and compute the inverse of two-by-two and three-by-three matrices when they exist.
  • Explain the role of determinants in solving systems of linear equations using matrices and compute determinants of two-by-two and three-by-three matrices.
  • Write systems of two and three linear equations in matrix form. Solve such systems using Gaussian elimination or inverse matrices.
  • Represent and solve systems of inequalities in two variables and apply these methods in linear
    programming situations to solve problems.
  • Recognize, explain, and use sigma and factorial notation.
  • Given an arithmetic, geometric, or recursively defined sequence, write an expression for the nth term when possible. Write a particular term of a sequence when given the nth term.
  • Explain, and use the formulas for the sums of finite arithmetic and geometric sequences.
  • Compute the sums of infinite geometric series. Apply the convergence criterion for geometric series.
  • Convert between polar and rectangular coordinates. Graph functions given in polar coordinates.
  • Write complex numbers in polar form. Know and use De Moivre’s Theorem.
  • Evaluate parametric equations for given values of the parameter.
  • Convert between parametric and rectangular forms of equations.
  • Graph curves described by parametric equations and find parametric equations for a given graph.
  • Explain and apply the locus definitions of parabolas, ellipses, and hyperbolas and recognize these conic sections in applied situations.
  • Identify parabolas, ellipses, and hyperbolas from equations, write the equations in standard form, and sketch an appropriate graph of the conic section.
  • Derive the equation for a conic section from given geometric information. Identify key characteristics of a conic section from its equation or graph.

INACOL Online Course Quality Standards

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Review Conducted By : Michigan Virtual
Date of Review : 04/02/2020

Unit 9: Polynomial Functions

Unit 10: Rational Functions

Unit 11: Exponential & Logarithmic Functions

Unit 12: Sequences & Series

Unit 13: Conics

Unit 14: Limits

Unit 15: Systems

Unit 16: Trigonometry & The Polar Plane

Term Type Enrollment Opens Enrollment Ends Random Draw Date Enrollment Drop Date Course Starts Course Ends # of Seats Course Fee Potential Additional Costs
Semester 08/01/2020 10/15/2020 07/01/2020 08/31/2020 01/15/2021 35 $0.0000 0.0000
Drop Policy Completion Policy Term Type Enrollment Opens Enrollment Ends
Consult counselor Consult counselor Semester 08/01/2020 10/15/2020

Students can use email or the private message system within the Student Learning Portal to access highly qualified teachers when they need instructor assistance. Students will also receive feedback on their work inside the learning management system. The Instructor Info area of their course may describe additional communication options.

Students will require a computer device with headphones, a microphone, webcam, up-to-date Chrome Web Browser, and access to YouTube. Students will also require a graphing calculator, such as TI-84 Plus, TI-83, or TI-83 Plus.

Please review the Michigan Virtual Technology Requirements: