Interpreting Functions

IA.FIF.3Define functions recursively and recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.IA.FIF.4Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity.IA.FIF.5Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.IA.FIF.6Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context.IA.FIF.7Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases.IA.FIF.8Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function. (Note: IA.FIF.8b is not a Graduation Standard.) b. Interpret expressions for exponential functions by using the properties of exponents.IA.FIF.9Compare properties of two functions given in different representations such as algebraic, graphical, tabular, or verbal.
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