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 In Topic B, students explore composition of functions in depth and notice that a composition of a polynomial function with the function f(x) = 1/x gives functions that can be written as ratios of...

 Student Outcomes Students reduce rational expressions to lowest terms. Students determine the domain of rational functions.

 Student Outcomes Students create exponential functions to model realworld situations. Students use logarithms to solve equations of the form f(t) = a ∙ bct for t. Students decide which type of model...

 Student Outcomes Students will compare payment strategies for a decreasing credit card balance. Students will apply the sum of a finite geometric series formula to a decreasing balance on a credit...

 Topic E is a culminating series of lessons driven by MP.4, Modeling with Mathematics. Students apply what they have learned about mathematical models and exponential growth to financial literacy...

 Topic D opens with a handson simulation and modeling activity in which students gather data and apply the analysis of Lesson 22 in Topic C to model it with an exponential function (ACED.2, FLE.5...

 Student Outcomes Students use geometric series to calculate how much money should be saved each month to have 1 million in assets within a specified amount of time.

 Student Outcomes Students model a crosssection of a riverbed with a polynomial function and estimate fluid flow with their algebraic model.

 Student Outcomes Students learn to fit polynomial functions to data values.

 Student Outcomes Students compare two different quadratic, square root, or cube root functions represented as graphs, tables, or equations. They interpret, contextualize and abstract various...

 Student Outcomes Students graph polynomial functions and describe end behavior based upon the degree of the polynomial.

 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 Student Outcomes Students will use the factored forms of polynomials to find zeros of a function. Students will use the factored forms of polynomials to sketch the components of graphs between zeros.

 Student Outcomes Students graph simple quadratic equations of the form y = a(x  h)2 + k (completedsquare or vertex form), recognizing that (h,k) represents the vertex of the graph and use a graph...

 Student Outcomes Students create piecewise and step functions that relate to reallife situations and use those functions to solve problems. Students interpret graphs of piecewise and step functions...

 In Topic C, students explore the families of functions that are related to the parent functions, specifically for quadratic (f(x) = x2), square root (f(x) = the square root of x), and cube root (f(x...

 Student Outcomes Students solve complex quadratic equations, including those with a leading coefficient other than 1, by completing the square. Some solutions may be irrational. Students draw...

 In Topic D, students apply and reinforce the concepts of the module as they examine and compare exponential, piecewise, and step functions in a realworld context (FIF.C.9). They create equations...

 This topic focuses on factoring polynomials and the advantages of factored form of a polynomial to both solve equations and sketch graphs of polynomial functions. Students solve problems involving...

 Student Outcomes Students discover that the multistep and exact way of solving 2x  5 = 3x + 1 using algebra can sometimes be avoided by recognizing that an equation of the form f(x) = g(x) can...

 Student Outcomes Students use the factored form of a quadratic equation to construct a rough graph, use the graph of a quadratic equation to construct a quadratic equation in factored form, and...

 Students apply their experiences from Topic A as they transform quadratic functions from standard form to vertex form, (x) = a(x  h)2 + k in Topic B. The strategy known as completing the square is...

 In Topic C, students extend their understanding of piecewise functions and their graphs including the absolute value and step functions. They learn a graphical approach to circumventing complex...

 Topic A introduces polynomial expressions. In Module 1, students learned the definition of a polynomial and how to add, subtract, and multiply polynomials. Here, their work with multiplication is...