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What grade level is F-IF taught?

This standard is part of the F-IF curriculum in Alaska Mathematics Standards.

Interpreting Functions Math Standards | Alaska | Alaska Mathematics Standards

Interpreting Functions

Interpreting Functions covers the core language of functions: domain, range, notation, and reading function behavior from graphs, tables, and formulas. Key families including linear, quadratic, polynomial, exponential, logarithmic, and trigonometric functions are analyzed for rate of change, intercepts, maxima and minima, and end behavior. Multiple representations are translated fluidly to build a unified picture of each function type.

F-IF.1Understand 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. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).F-IF.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.F-IF.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.F-IF.4For 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.F-IF.5Relate 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 person-hours it takes to assemble n engines in a factory, then negative numbers would be an appropriate domain for the function.F-IF.6Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.F-IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.F-IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.F-IF.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Example Problems

What is the inverse of the function?

f(x) = 8x + 1

Find

\frac{d}{dx}(e^{\tan(4x)})

f(x) = 3 + 4(x - 1)

Find the fourth term in the sequence.

Find

\frac{d}{dx}(\cos(x) - 7x)

Find

\lim_{x \to 0} \frac{-8}{x^3}

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F-IF: Interpreting Functions

Interpreting Functions