PC.F: Functions

PC.F.1: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Cosine Function
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Sine Function
Standard Form of a Line
Tangent Function
Translating and Scaling Sine and Cosine Functions

PC.F.2: Find linear models by using median fit and least squares regression methods, making use of technology. Decide which among several linear models gives a better fit. Interpret the slope and intercept in terms of the original context.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

PC.F.4: Determine if a graph or table has an inverse, and justify if the inverse is a function, relation, or neither. Identify the values of an inverse function/relation from a graph or a table, given that the function has an inverse. Derive the inverse equation from the values of the inverse.

Logarithmic Functions
Radical Functions

PC.F.6: Recognize even and odd functions from their graphs and algebraic expressions.

Cosine Function
Sine Function
Tangent Function

PC.QPR: Quadratic, Polynomial and Rational Equations and Functions

PC.QPR.1: Use the method of completing the square to transform any quadratic equation into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.

Roots of a Quadratic

PC.QPR.2: Understand and use addition, subtraction, multiplication, and conjugation of complex numbers.

Points in the Complex Plane

PC.QPR.3: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

Points in the Complex Plane

PC.QPR.4: Know and apply the Remainder Theorem and the Factor Theorem.

Dividing Polynomials Using Synthetic Division

PC.QPR.5: Understand the Fundamental Theorem of Algebra. Find a polynomial function of lowest degree with real coefficients when given its roots.

Polynomials and Linear Factors

PC.QPR.6: Graph rational functions with and without technology. Identify and describe features such as intercepts, domain and range, and asymptotic and end behavior.

General Form of a Rational Function
Rational Functions

PC.EL: Exponential and Logarithmic Functions

PC.EL.2: Use the laws of logarithms to simplify logarithmic expressions, approximate the value of a logarithmic expression, and solve logarithmic equations.

Logarithmic Functions
Logarithmic Functions: Translating and Scaling

PC.EL.3: Graph and solve real-world and other mathematical problems that can be modeled using exponential and logarithmic functions; interpret the solution and determine whether it is reasonable. Identify and describe features such as intercepts, domain, range, asymptotes, and end behavior.

Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling

PC.SS: Sequences and Series

PC.SS.1: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

PC.SS.2: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms.

Arithmetic Sequences
Geometric Sequences

PC.SS.4: Model and solve real-world problems involving applications of sequences and series, interpret the solutions and determine whether the solutions are reasonable.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

PC.CO: Conics

PC.CO.1: Construct the equation of a parabola given a focus and directrix.

Parabolas

PC.CO.2: Construct the equation of a circle of given center and radius. Complete the square to find the center and radius of a circle given by an equation.

Circles

PC.CO.3: Construct the equations of ellipses and hyperbolas given at least 2 of the following: foci, vertices, length of an axis, or point on the curve.

Ellipses
Hyperbolas

PC.CO.4: Graph conic sections. Identify and describe features like center, vertex or vertices, focus or foci, directrix, axis of symmetry, major axis, minor axis, and eccentricity.

Circles
Ellipses
Hyperbolas
Parabolas