Units
Unit 3: Functions and their Graphs (3 days)
TEKS/SEs
Unit 3: Functions and their Graphs (3 days)
P.2.N Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve realworld problems
P.2.F Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
P.2.N Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve realworld problems
P.2.A Use the composition of two functions to model and solve realworld problems
P.2.B Demonstrate that function composition is not always commutative
P.2.C Represent a given function as a composite function of two or more functions
P.2.E Determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations
P.2.N Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve realworld problems
P.2.F Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
P.2.G Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d, in mathematical and realworld problems
P.2.I Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
P.2.J Analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and realworld problems
P.2.N Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve realworld problems
P.2.F Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
P.2.G Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d, in mathematical and realworld problems
P.2.I Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
P.2.J Analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and realworld problems
P.2.L Determine various types of discontinuities in the interval (∞, ∞) as they relate functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities
P.2.N Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve realworld problems
P.5.J Solve polynomial equations with real coefficients by applying a variety of techniques in mathematical and realworld problems
P.2.I Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
P.2.N Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve realworld problems
P.5.J Solve polynomial equations with real coefficients by applying a variety of techniques in mathematical and realworld problems
P.2.F Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
P.2.G Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d, in mathematical and realworld problems
P.2.I Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
P.2.J Analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and realworld problems
P.2.L Determine various types of discontinuities in the interval (∞, ∞) as they relate functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities
P.2.M Describe the leftsided behavior and the rightsided behavior of the graph of a function around discontinuities
P.2.N Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve realworld problems
P.5.K Solve polynomial inequalities with real coefficients by applying a variety of techniques and write the solution set of the polynomial inequality in interval notation in mathematical and realworld
P.5.L Solve rational inequalities with real coefficients by applying a variety of techniques and write the solution set of the rational inequality in interval notation in mathematical and realworld problems
Students will use problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution and evaluating the problemsolving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Units
Unit 4: Exponential/Log Functions and Conics (42 days)
TEKS/SEs
Unit 4: Exponential/Log Functions and Conics (42 days)
P.2.F Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
P.2.G Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d, in mathematical and realworld problems
P.2.I Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
P.2.J Analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and realworld problems
P.2.N Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve realworld problems
P.2.N Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve realworld problems
P.5.G Use the properties of logarithms to evaluate ore transform logarithmic expressions
P.5.H Generate and solve logarithmic equations in mathematical and realworld problems
P.5.I Generate and solve exponential equations in mathematical and realworld problems
P.5.A Evaluate finite sums and geometric series, when possible, written in sigma notation
P.5.B Represent arithmetic sequences and geometric sequences using recursive formulas
P.5.D Represent arithmetic series and geometric series using sigma notation
P.1.A Apply mathematics to problems arising in everyday life, society, and the workplace
P.1.B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution
P.1.C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
P.1.D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
P.1.E Create and use representations to organize, record, and communicate mathematical ideas
P.1.F Analyze mathematical relationships to connect and communicate mathematical ideas
P.1.G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
P.1.A Apply mathematics to problems arising in everyday life, society, and the workplace
P.1.B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution
P.1.C Select tools, including real objects, manipulative, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
P.1.D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
P.1.E Create and use representations to organize, record, and communicate mathematical ideas
P.1.F Analyze mathematical relationships to connect and communicate mathematical ideas
P.1.G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
P.3.G Make connections between the locus definition of conic sections and their equations in rectangular coordinates
P.3.G Make connections between the locus definition of conic sections and their equations in rectangular coordinates
P.3.H Use the characteristics of an ellipse to write the equation of an ellipse with center (h, k)
P.3.I Use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k)
Students will use problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution and evaluating the problemsolving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

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