Category: Algebra II TEKS

8A analyze data to select the appropriate model from among linear, quadratic, and exponential models

8B use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data

8C predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models

7A add, subtract, and multiply complex numbers

7B add, subtract, and multiply polynomials

7C determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two

7D determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods

7E determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping

7F determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two

7G rewrite radical expressions that contain variables to equivalent forms

7H solve equations involving rational exponents

7I write the domain and range of a function in interval notation, inequalities, and set notation

 

6A analyze the effect on the graphs of f(x) = x³ and f(x) = ³√x when f(x) is replaced by af(x), f(bx), f(x – c), and f(x) + d for specific positive and negative real values of a, b, c, and d

6B solve cube root equations that have real roots

6C analyze the effect on the graphs of f(x) = |x| when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d

6D formulate absolute value linear equations

6E solve absolute value linear equations

6F solve absolute value linear inequalities

6G analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d

6H formulate rational equations that model real-world situations

6I solve rational equations that have real solutions

6J determine the reasonableness of a solution to a rational equation

6K determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation

6L formulate and solve equations involving inverse variation

5A determine the effects on the key attributes on the graphs of f(x) = b to the x power and f(x) = logb (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x – c) for specific positive and negative real values of a, c, and d

5B formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation

5C rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations

5D solve exponential equations of the form y = ab to the x power where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions

5E determine the reasonableness of a solution to a logarithmic equation

4A write the quadratic function given three specified points in the plane

4B write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening

4C determine the effect on the graph of f(x) = √x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x – c) for specific positive and negative values of a, b, c, and d

4D transform a quadratic function f(x) = ax² + bx + c to the form f(x) = a(x – h)² + k to identify the different attributes of f(x)

4E formulate quadratic and square root equations using technology given a table of data

4F solve quadratic and square root equations

4G identify extraneous solutions of square root equations

4H solve quadratic inequalities

3A formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic

3B solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution

3C solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation

3D determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables

3E formulate systems of at least two linear inequalities in two variables

3F solve systems of two or more linear inequalities in two variables

3G determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.

2A The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse.

2B graph and write the inverse of a function using notation such as f-¹ (x);

2C describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range

2D use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.