Attributes of Functions and Their Inverses
Students understand that functions have distinct key attributes and understand the relationship between a function and its inverse.
- Graph and analyze key attributes of cube and cube root functions
- Analyze “key attributes” of functions (domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum)
- Use inverse function notation f-1(x)
- Use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other
Systems of Equations and Inequalities
Students formulate systems of equations and inequalities, use a variety of methods to solve and analyze reasonableness of solutions.
- Formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations (one linear and one quadratic)
- Solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution
- Solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation
Quadratic and Square Root Functions, Equations, and Inequalities
Students understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions.
- Write the equation of a parabola using given attributes (vertex, focus, directrix, axis of symmetry, and direction of opening)
- Identify extraneous solutions of square root equations
Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities
Students understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions.
- Analyze the effect of parameter changes to the cube, cube root, and absolute value functions
- Solve cube root equations that have real roots
- Formulate absolute value linear equations
- Solve absolute value linear equations
- Solve absolute value linear inequalities
Number and Algebraic Methods
Students simplify and perform operations on expressions and to solve equations.
- Add, subtract, and multiply complex numbers
- Add, subtract, and multiply polynomials
- Divide polynomials (3rd and 4th degree)
- Factor polynomials (3rd and 4th degree) using algebraic methods and including sum and difference of 2 cubes and factoring by grouping
- Rewrite radical expressions that contain variables to equivalent forms
- Solve equations involving rational exponents
- Write domain and range of a function in interval notation, inequalities, and set notation