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Common Core: Math
CCLS  Math: F.IF.5
 Category
 Interpreting Functions
 SubCategory
 Interpret Functions That Arise In Applications In Terms Of The Context
 State Standard:
 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★
22 Results

 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...

 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 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 compare linear and exponential models by focusing on how the models change over intervals of equal length. Students observe from tables that a function that grows...

 Student Outcomes Students create tables and graphs of functions and interpret key features including intercepts, increasing and decreasing intervals, and positive and negative intervals.

 Student Outcomes Students understand the meaning of the graph of y = f(x), namely {(x,y)  x ∈ D and y = f(x)}. Students understand the definitions of when a function is increasing or decreasing.

 Student Outcomes Students understand set builder notation for the graph of a realvalued function: {(x, f(x))  x ∈ D}. Students learn techniques for graphing functions and relate the domain of a...

 Student Outcomes Students use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Students create functions...

 Algebra I Module 5: A Synthesis of Modeling with Equations and Functions In Module 5, students synthesize what they have learned during the year about functions to select the correct function type in...

 Algebra I Module 4: Polynomial and Quadratic Expressions, Equations, and Functions In earlier modules, students analyze the process of solving equations and developing fluency in writing,...

 Algebra I Module 3: Linear and Exponential Functions In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module,...