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Texas TEKS Algebraic Reasoning
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(Random) 2.A Patterns and structure. Determine the patterns that identify the relationship between a function and its common ratio or related finite differences as appropriate, including linear, quadratic, cubic, and exponential functions

(Random) 2.B Patterns and structure. Classify a function as linear, quadratic, cubic, and exponential when a function is represented tabularly using finite differences or common ratios as appropriate; (Random) 2.C Patterns and structure. Determine the function that models a given table of related values using finite differences and its restricted domain and range; and (Random) 2.D Determine a function that models real-world data and mathematical contexts using finite differences. (Random) 3.A Patterns and structure. Compare and contrast the key attributes, including domain, range, maxima, minima, and intercepts, of a set of functions (Random) 3.B Patterns and structure. Compare and contrast the key attributes of a function and its inverse when it exists. (Random) 3.C Patterns and structure. Verify that two functions are inverses of each other tabularly and graphically. (Random) 3.D Patterns and structure. Represent a resulting function tabularly, graphically, and symbolically when functions are combined or separated using arithmetic operations (Random) 3.E Patterns and structure. Model a situation using function notation when the output of one function is the input of a second function (Random) 3.F Patterns and structure. Compare and contrast a function and possible functions that can be used to build it tabularly, graphically, and symbolically (Random) 4.A Number and algebraic methods. Connect tabular representations to symbolic representations when adding, subtracting, and multiplying polynomial functions arising from mathematical and real-world situations. (Random) 4.B Number and algebraic methods. Compare and contrast the results when adding two linear functions and multiplying two linear functions that are represented tabularly, graphically, and symbolically;

(Random) 4.C Number and algebraic methods. Determine the quotient of a polynomial function of degree three and of degree four when divided by a polynomial function of degree one and of degree two when represented tabularly and symbolically; and (Random) 4.D Number and algebraic methods. Determine the linear factors of a polynomial function of degree two and of degree three when represented symbolically and tabularly and graphically where appropriate. (Random) 5.A Number and algebraic methods. Add and subtract matrices; (Random) 5.B Number and algebraic methods. Multiply matrices; (Random) 5.C Number and algebraic methods. Multiply matrices by a scalar; (Random) 5.D Number and algebraic methods. Represent and solve systems of two linear equations arising from mathematical and real-world situations using matrices; and (Random) 5.E Number and algebraic methods. Represent and solve systems of three linear equations arising from mathematical and real-world situations using matrices and technology. (Random) 6.A Number and algebraic methods. Estimate a reasonable input value that results in a given output value for a given function, including quadratic, rational, and exponential functions; (Random) 6.B Number and algebraic methods. Solve equations arising from questions asked about functions that model real-world applications, including linear and quadratic functions, tabularly, graphically, and symbolically; and (Random) 6.C Number and algebraic methods. Approximate solutions to equations arising from questions asked about exponential, logarithmic, square root, and cubic functions that model real-world applications tabularly and graphically. (Random) 7.A Modeling from data. Represent domain and range of a function using interval notation, inequalities, and set (builder) notation; (Random) 7.B Modeling from data. Compare and contrast between the mathematical and reasonable domain and range of functions modeling real-world situations, including linear, quadratic, exponential, and rational functions; (Random) 7.C Modeling from data. Determine the accuracy of a prediction from a function that models a set of data compared to the actual data using comparisons between average rates of change and finite differences (Random) 7.D Modeling from data. Determine an appropriate function model, including linear, quadratic, and exponential functions, for a set of data arising from real-world situations using finite differences and average rates of change; and (Random) 7.E Modeling from data. Determine if a given linear function is a reasonable model for a set of data arising from a real-world situation.

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