)TXTX��TX��TXTbTX��TXm{TX�TX��TX��TX��TXTXm{TXTXlzTX��TX	+	TX�		
TX�
�
TX�
TX��TX��TXy
�
TX,:TX��TX2@TX#TX��TX��TX"TX��TX-<TX,TX��TX~�TXTX��TX8GTX��TX�TX�TX��TX TEKS 2A.1AThe student is expected to identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations; andTX TEKS 2A.1BThe student is expected to collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.TX TEKS 2A.2AThe student is expected to use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations; andTX TEKS 2A.2BThe student is expected to use complex numbers to describe the solutions of quadratic equations.TX TEKS 2A.3AThe student is expected to analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems;TX TEKS 2A.3BThe student is expected to use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities; andTX TEKS 2A.3CThe student is expected to interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.TX TEKS 2A.4AThe student is expected to identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x2); exponential; f(x) = ax, and logarithmic  (f(x) = logax) functions, absolute value of x (f(x) = |x|), square root of x (f(x) = �x), and reciprocal of x (f(x) = 1/x);TX TEKS 2A.4BThe student is expected to extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions; andTX TEKS 2A.4CThe student is expected to describe and analyze the relationship between a function and its inverse.TX TEKS 2A.5AThe student is expected to describe a conic section as the intersection of a plane and a cone;TX TEKS 2A.5BThe student is expected to sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph;TX TEKS 2A.5CThe student is expected to identify symmetries from graphs of conic sections;TX TEKS 2A.5DThe student is expected to identify the conic section from a given equation; andTX TEKS 2A.5EThe student is expected to use the method of completing the square.TX TEKS 2A.6AThe student is expected to determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;TX TEKS 2A.6BThe student is expected to relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions; andTX TEKS 2A.6CThe student is expected to determine a quadratic function from its roots or a graph.TX TEKS 2A.7AThe student is expected to use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax2 + bx + c and the y = a(x - h)2 + k symbolic representations of quadratic functionsTX TEKS 2A.7BThe student is expected to use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)2 + k form of a function in applied and purely mathematical situations.TX TEKS 2A.8AThe student is expected to analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems;TX TEKS 2A.8BThe student is expected to analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;TX TEKS 2A.8CThe student is expected to compare and translate between algebraic and graphical solutions of quadratic equations; andTX TEKS 2A.8DThe student is expected to solve quadratic equations and inequalities using graphs, tables, and algebraic methods.TX TEKS 2A.9AThe student is expected to use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges;TX TEKS 2A.9BThe student is expected to relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions;TX TEKS 2A.9CThe student is expected to determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities;TX TEKS 2A.9DThe student is expected to determine solutions of square root equations using graphs, tables, and algebraic methods;TX TEKS 2A.9FThe student is expected to analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems; andTX TEKS 2A.9GThe student is expected to connect inverses of square root functions with quadratic functions.TX TEKS 2A.10AThe student is expected to use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior;TX TEKS 2A.10BThe student is expected to analyze various representations of rational functions with respect to problem situations;TX TEKS 2A.10CThe student is expected to determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities;TX TEKS 2A.10DThe student is expected to determine the solutions of rational equations using graphs, tables, and algebraic methods;TX TEKS 2A.10FThe student is expected to analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem; andTX TEKS 2A.10GThe student is expected to use functions to model and make predictions in problem situationsTX TEKS 2A.11AThe student is expected to develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses;TX TEKS 2A.11BThe student is expected to use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;TX TEKS 2A.11CThe student is expected to determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities;TX TEKS 2A.11DThe student is expected to determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods;TX TEKS 2A.11FThe student is expected to analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.