Overview
Addressed HSCEs
The following Michigan High School Content Expectations will be addressed within this unit.
A1.1.1 Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables.
A1.2.1 Write and solve equations and inequalities with one or two variables to represent mathematical or applied situations.
A1.2.2 Associate a given equation with a function whose zeros are the solutions of the equation.
A1.2.3 Solve linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns. Justify steps in the solutions, and apply the quadratic formula appropriately.
A1.2.8 Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable. Justify steps in the solution.
A2.1.1 Recognize whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a function and identify its domain and range.
A2.1.2 Read, interpret, and use function notation and evaluate a function at a value in its domain.
A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words and translate among representations.
A2.1.6 Identify the zeros of a function and the intervals where the values of a function are positive or negative. Describe the behavior of a function as x approaches positive or negative infinity, given the symbolic and graphical representations.
A2.1.7 Identify and interpret the key features of a function from its graph or its formula(e), (e.g., slope, intercept(s), asymptote(s), maximum and minimum value(s), symmetry, and average rate of change over an interval).
A2.2.1 Combine functions by addition, subtraction, multiplication, and division.
A2.2.2 Apply given transformations (e.g., vertical or horizontal shifts, stretching or shrinking, or reflections about the x- and y-axes) to basic functions and represent symbolically.
A2.2.3 Recognize whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs.
A2.3.2 Describe the tabular pattern associated with functions having a constant rate of change (linear) or variable rates of change.
A2.4.2 Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers.
A2.4.3 Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled.
L1.1.2 Explain why the multiplicative inverse of a number has the same sign as the number, while the additive inverse has the opposite sign.
L1.1.3 Explain how the properties of associativity, commutativity, and distributivity, as well as identity and inverse elements, are used in arithmetic and algebraic calculations.