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Texas TEKS Algebra II
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(Random) (2.A) Attributes of functions and their inverses. Graph the functions f(x)=√x, f(x)=1/x, f(x)=x3, f(x)=3√x, f(x)=bx, f(x)=|x|, and f(x)=logb(x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range

(Random) (2.A) Attributes of functions and their inverses. Graph the functions f(x)=√x, f(x)=1/x, f(x)=x3, f(x)=3√x, f(x)=bx, f(x)=|x|, and f(x)=logb(x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as intercepts (Random) (2.A) Attributes of functions and their inverses. Graph the functions f(x)=√x, f(x)=1/x, f(x)=x3, f(x)=3√x, f(x)=bx, f(x)=|x|, and f(x)=logb(x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as symmetries (Random) (2.A) Attributes of functions and their inverses. Graph the functions f(x)=√x, f(x)=1/x, f(x)=x3, f(x)=3√x, f(x)=bx, f(x)=|x|, and f(x)=logb(x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as asymptotic behavior (Random) (2.A) Attributes of functions and their inverses. Graph the functions f(x)=√x, f(x)=1/x, f(x)=x3, f(x)=3√x, f(x)=bx, f(x)=|x|, and f(x)=logb(x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as maximum and minimum given an interval; (Random) (2.B) Attributes of functions and their inverses. Graph and write the inverse of a function using notation such as f-1(x); (Random) (2.C) Attributes of functions and their inverses. 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; (Random) (2.D) Attributes of functions and their inverses. Use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other. (Random) (3.A) Systems of equations and inequalities. 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; (Random) (3.B) Systems of equations and inequalities. Solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution; (Random) (3.C) Systems of equations and inequalities. Solve algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation; (Random) (3.D) Systems of equations and inequalities. Determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables; (Random) (3.E) Systems of equations and inequalities. Formulate systems of at least two linear inequalities in two variables; (Random) (3.F) Systems of equations and inequalities. Solve systems of two or more linear inequalities in two variables; (Random) (3.G) Systems of equations and inequalities. Determine possible solutions in the solution set of systems of two or more linear inequalities in two variables. (Random) (4.A) Quadratic and square root functions. Write the quadratic function given three specified points in the plane; (Random) (4.B) Quadratic and square root functions. Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening; (Random) (4.C) Quadratic and square root functions. 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; (Random) (4.D) Quadratic and square root functions. 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); (Random) (4.E) Quadratic and square root functions. Formulate quadratic and square root equations using technology given a table of data; (Random) (4.F) Quadratic and square root functions. Solve quadratic and square root equations; (Random) (4.G) Quadratic and square root functions. Identify extraneous solutions of square root equations; (Random) (4.H) Quadratic and square root functions. Solve quadratic inequalities. (Random) (5.A) Exponential and logarithmic functions. Determine the effects on the key attributes on the graphs of f(x) = bx 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;
(Random) (5.B) Exponential and logarithmic functions. Formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation; (Random) (5.C) Exponential and logarithmic functions. Rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations; (Random) (5.D) Exponential and logarithmic functions. Solve exponential equations of the form y = abx 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; (Random) (5.E) Exponential and logarithmic functions. Determine the reasonableness of a solution to a logarithmic equation. (Random) (6.A) Cubic, cube root, absolute value and rational functions. 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; (Random) (6.B) Cubic, cube root, absolute value and rational functions. Solve cube root equations that have real roots; (Random) (6.C) Cubic, cube root, absolute value and rational functions. 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; (Random) (6.D) Cubic, cube root, absolute value and rational functions. Formulate absolute value linear equations; (Random) (6.E) Cubic, cube root, absolute value and rational functions. Solve absolute value linear equations; (Random) (6.F) Cubic, cube root, absolute value and rational functions. Solve absolute value linear inequalities; (Random) (6.G) Cubic, cube root, absolute value and rational functions. 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; (Random) (6.H) Cubic, cube root, absolute value and rational functions. Formulate rational equations that model real-world situations; (Random) (6.I) Cubic, cube root, absolute value and rational functions. Solve rational equations that have real solutions; (Random) (6.J) Cubic, cube root, absolute value and rational functions. Determine the reasonableness of a solution to a rational equation; (Random) (6.K) Cubic, cube root, absolute value and rational functions. Determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation; (Random) (6.L) Cubic, cube root, absolute value and rational functions. Formulate and solve equations involving inverse variation. (Random) (7.A) Number and algebraic methods. Add, subtract, and multiply complex numbers; (Random) (7.B) Number and algebraic methods. Add, subtract, and multiply polynomials; (Random) (7.C) Number and algebraic methods. 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; (Random) (7.D) Number and algebraic methods. Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods; (Random) (7.E) Number and algebraic methods. 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; (Random) (7.F) Number and algebraic methods. Determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two; (Random) (7.G) Number and algebraic methods. Rewrite radical expressions that contain variables to equivalent forms; (Random) (7.H) Number and algebraic methods. Solve equations involving rational exponents; (Random) (7.I) Number and algebraic methods. Write the domain and range of a function in interval notation, inequalities, and set notation. (Random) (8.A) Data. Analyze data to select the appropriate model from among linear, quadratic, and exponential models; (Random) (8.B) Data. Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data; (Random) (8.C) Data. Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.

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