Algebra II

  • Attributes of Functions and Their Inverses

    Students understand that functions have distinct key attributes and understand the relationship between a function and its inverse.

    New TEKS:

    • 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.

    New TEKS:

    • 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.

    New TEKS:

    • 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. 

    New TEKS:

    • 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.

    New TEKS:

    • 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