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### 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.
- 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.
- PC.F.3 Compose functions and find the domain of composite functions.
- 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.
- PC.F.5 Produce an invertible function from a non-invertible function by restricting the domain.
- PC.F.6 Describe the effect on the graph of replacing
*f(x)*by*f(x) + k*,*kf(x)*,*f(kx)*, and*f(x + k)*for specific values of*k*(both positive and negative). Find the value of*k*given the graph*f(x)*and the graph of*f(x) + k*,*kf(x)*,*f(kx)*, or*f(x + k)*. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Recognize even and odd functions from their graphs and algebraic expressions.

### 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. - PC.QPR.2 Understand and use addition, subtraction, multiplication, and conjugation of complex numbers.
- 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.
- PC.QPR.4 Know and apply the Remainder Theorem and the Factor Theorem.
- PC.QPR.5 Understand the Fundamental Theorem of Algebra. Find a polynomial function of lowest degree with real coefficients when given its roots.
- 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.

### PC.EL Exponential and Logarithmic Functions

- PC.EL.1 Use the definition of logarithms to convert logarithms from one base to another and prove simple laws of logarithms.
- PC.EL.2 Use the laws of logarithms to simplify logarithmic expressions, approximate the value of a logarithmic expression, and solve logarithmic equations.
- 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.
- PC.EL.4 Use technology to find a quadratic, exponential, logarithmic, or power function that models a relationship for a bivariate data set to make predictions.

### PC.SS Sequences and Series

- PC.SS.1 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
- 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.
- PC.SS.3 Find partial sums of arithmetic and geometric series and represent them using sigma notation.
- 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.

### PC.CO Conics

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