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Common Core: Standard
Common Core: ELA
Common Core: Math
CCLS  Math: F.IF.4
 Category
 Interpreting Functions
 SubCategory
 Interpret Functions That Arise In Applications In Terms Of The Context
 State Standard:
 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★
32 Results

 Student Outcomes Students understand that the change of base property allows us to write every logarithm function as a vertical scaling of a natural logarithm function. Students graph the natural...

 Student Outcomes Students study transformations of the graphs of logarithmic functions. Students use the properties of logarithms and exponents to produce equivalent forms of exponential and...

 Student Outcomes Students will understand that the logarithm function base b and the exponential function base b are inverse functions.

 Student Outcomes Students compare the graph of an exponential function to the graph of its corresponding logarithmic function. Students note the geometric relationship between the graph of an...

 Student Outcomes Students graph the functions f(x) = log(x), g(x) = log2(x), and h(x) = ln(x) by hand and identify key features of the graphs of logarithmic functions.

 In Topic C, students graph logarithmic functions, identifying key features (FIF.4, FIF.7) and discover how the logarithmic properties are evidenced in the graphs of corresponding logarithmic...

 Exponential and Logarithmic Functions In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions...

 Tables, graphs, and equations all represent models. We use terms such as “symbolic” or “analytic” to refer specifically to the equation form of a function model; “descriptive model” refers to a...

 Topic A focuses on the skills inherent in the modeling process: representing graphs, data sets, or verbal descriptions using explicit expressions (FBF.A.1a) when presented in graphic form in Lesson...

 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...

 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...

 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...

 In Topic B, students connect their understanding of functions to their knowledge of graphing from Grade 8. They learn the formal definition of a function and how to recognize, evaluate, and...

 Student Outcomes Students interpret the function and its graph and use them to answer questions related to the model, including calculating the rate of change over an interval, and always using an...

 Student Outcomes Students model functions described verbally in a given context using graphs, tables, or algebraic representations.

 Student Outcomes Students write equations to model data from tables, which can be represented with linear, quadratic, or exponential functions, including several from Lessons 4 and 5. They recognize...

 Student Outcomes Students create a twovariable equation that models the graph from a context. Function types include linear, quadratic, exponential, square root, cube root, and absolute value. ...

 Student Outcomes Students make sense of a contextual situation that can be modeled with linear, quadratic, and exponential functions when presented as a word problem. They analyze a verbal...

 Student Outcomes Students recognize linear, quadratic, and exponential functions when presented as a data set or sequence, and formulate a model based on the data.

 Student Outcomes From a graphic representation, students recognize the function type, interpret key features of the graph, and create an equation or table to use as a model of the context for...

 Student Outcomes Students graph a variety of quadratic functions using the form f(x) = ax2 + bx + c (standard form). Students analyze and draw conclusions about contextual applications using the key...

 Student Outcomes Students interpret quadratic functions from graphs and tables: zeros (xintercepts), yintercept, the minimum or maximum value (vertex), the graph’s axis of symmetry, positive and...

 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...

 Student Outcomes Students examine quadratic equations in two variables represented graphically on a coordinate plane and recognize the symmetry of the graph. They explore key features of graphs of...