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Functions: Interpreting Functions

2112 questions103 skills


215 questions10 skills
Understand 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).


102 questions5 skills
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.


177 questions8 skills
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.


46 questions3 skills
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.


76 questions3 skills
Calculate 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.


730 questions41 skills
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.


92 questions6 skills
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.


47 questions3 skills
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.


66 questions4 skills
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.


101 questions4 skills
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).