Algebra

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

Identify and interpret parts of a piecewise, absolute value, polynomial, exponential and rational expressions including terms, factors, coefficients, and exponents.

Interpret expressions composed of multiple parts by viewing one or more of their parts as a single entity to give meaning in terms of a context.

Use the structure of an expression to identify ways to write equivalent expressions.

Write an equivalent form of an exponential expression by using the properties of exponents to transform expressions to reveal rates based on different intervals of the domain.

Understand and apply the Remainder Theorem.

Understand the relationship among factors of a polynomial expression, the solutions of a polynomial equation and the zeros of a polynomial function.

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 𝑟(𝑥) are polynomials with the degree of 𝑟(𝑥) less than the degree of 𝑏(𝑥).

Understand the similarities between arithmetic with rational expressions and arithmetic with rational numbers.

Add and subtract two rational expressions, 𝑎(𝑥) and 𝑏(𝑥), where the denominators of both 𝑎(𝑥) and 𝑏(𝑥) are linear expressions.

Multiply and divide two rational expressions.

Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically.

Create and graph equations in two variables to represent absolute value, polynomial, exponential and rational relationships between quantities.

Create systems of equations and/or inequalities to model situations in context.

Justify a solution method for equations and explain each step of the solving process using mathematical reasoning.

Solve and interpret one variable rational equations arising from a context, and explain how extraneous solutions may be produced.

Extend an understanding that the 𝑥-coordinates of the points where the graphs of two equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥) and approximate solutions using a graphing technology or successive approximations with a table of values.