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

Additional Cost Description: None

• 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.

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

Please review the Michigan Virtual Technology Requirements: https://michiganvirtual.org/about/support/knowledge-base/technical-requirements/