NC.M1.F-IF

Functions: Interpreting Functions

NC.M1.F-IF.1Build an understanding that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range by recognizing that:NC.M1.F-IF.1aIf f is a function and x is an element of its domain, then (x) denotes the output of f corresponding to the input x.NC.M1.F-IF.1bThe graph of f is the graph of the equation y = (x).NC.M1.F-IF.2Use function notation to evaluate linear, quadratic, and exponential functions for inputs in their domains, and interpret statements that use function notation in terms of a context.NC.M1.F-IF.3Recognize that recursively and explicitly defined sequences are functions whose domain is a subset of the integers, the terms of an arithmetic sequence are a subset of the range of a linear function, and the terms of a geometric sequence are a subset of the range of an exponential function.NC.M1.F-IF.4Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities, including: intercepts; intervals where the function is increasing, decreasing, positive, or negative; and maximums and minimums.NC.M1.F-IF.5Interpret a function in terms of the context by relating its domain and range to its graph and, where applicable, to the quantitative relationship it describes.NC.M1.F-IF.6Calculate and interpret the average rate of change over a specified interval for a function presented numerically, graphically, and/or symbolically.NC.M1.F-IF.7Analyze linear, exponential, and quadratic functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features, including: domain and range; rate of change; intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and end behavior.NC.M1.F-IF.8Use equivalent expressions to reveal and explain different properties of a function.NC.M1.F-IF.8aRewrite a quadratic function to reveal and explain different key features of the function.NC.M1.F-IF.8bInterpret and explain growth and decay rates for an exponential function.NC.M1.F-IF.9Compare key features of two functions (linear, quadratic, or exponential) each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions).
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