Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.*

(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.*

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.*

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the [...]

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry [...]

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions [...]

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [...]

Write a function that describes a relationship between two quantities.*

Determine an explicit expression, a recursive process, or steps for calculation from a context.

Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 [...]

(+) Know and apply that the Binomial Theorem gives the expansion of (x + y)^n in powers of x and [...]

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and [...]

(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division [...]

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic [...]

Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph [...]

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable [...]

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s [...]

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, [...]

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Solve quadratic equations in one variable.

Use the method of completing the square to transform any quadratic equation in x into an equation of the form [...]

Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and [...]

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation [...]

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For [...]

(+) Represent a system of linear equations as a single matrix equation in a vector variable.

(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using [...]

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the [...]

(+) Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that [...]

(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role [...]

(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another [...]

(+) Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant [...]

(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are [...]

(+) Add, subtract, and multiply matrices of appropriate dimensions.

(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies [...]

Interpret expressions that represent a quantity in terms of its context.*

Interpret parts of an expression, such as terms, factors, and coefficients.*

Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as [...]

Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 [...]

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the [...]

Factor a quadratic expression to reveal the zeros of the function it defines.

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Use the properties of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 [...]

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use [...]

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, [...]

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x [...]

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the [...]

Define appropriate quantities for the purpose of descriptive modeling.*