Course 2, Unit 1 - Functions, Equations, and Systems

Overview
This first algebra and functions unit of Course 2 builds on the units of Course 1 that developed student understanding of functions and their representation in tables, graphs, and symbolic rules and the particular properties of linear, exponential, and quadratic functions. The first lesson provides a review of those concepts and skills. The subsequent lessons are designed to extend algebraic thinking and problem solving to functions and equations involving several independent variables and finally systems of linear equations with two variables.

Key Ideas from Course 2, Unit 1

• Direct variation: If the relationship of variables y and x can be expressed in the form y = kx for some constant k, then we say that y varies directly with x or that y is directly proportional to x. The number k is called the constant of proportionality for the relationship. (See p. 7.)

• Inverse variation: If the relationship of variables y and x can be expressed in the form y = k/x for some constant k, then we say that y varies inversely with x or that y is directly proportional to x. The number k is called the constant of proportionality for the relationship. (See p. 7.)

• Direct variation power functions: power functions of the form y = axⁿ (n > 0)

• Inverse variation power functions: power functions of the form y = k/xⁿ (n > 0)

• Multiple-variable relationships: Ohm's Law is one multiple-variable relationship that students consider. Current I, voltage V, and resistance R are related in the relationship I = V/R. Students consider how keeping one variable constant and changing a second variable affects the third variable. They also rewrite multiple-variable formulas by solving for each variable. For example, I = V/R can also be written as I*R = V.

• Solving linear systems of equations: Solving a system of linear equations means finding ordered pair(s) of values that satisfies both linear equations. Linear systems have either no solutions, one solution, or infinitely many solutions. Graphically, the two lines will either be parallel, intersect in one point, or have the same graph (represent the same line). Algebraic methods for solving linear systems developed in this unit are the substitution method and the linear combination method. The matrix method for solving systems is developed in Unit 2.