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Основно съдържание

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Math

Kansas Math

Functions: Interpreting Functions

Understand the concept of a function and use function notation.

F.IF.1

Fully covered
(all) 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).

F.IF.2

Fully covered
(all) Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

F.IF.3

Fully covered
(9/10/11) Recognize patterns in order to write functions whose domain is a subset of the integers. (9/10) Limited to linear and quadratic. For example, find the function given {(−1,4),(0,7),(1,10),(2,13)}.

Interpret functions that arise in applications in terms of the context.

F.IF.4

Partially covered
(all) For a function that models a relationship between two quantities, interpret key features of expressions, graphs and tables in terms of the quantities, and sketch graphs showing key features given a 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.5

Fully covered
(all) 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 person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

F.IF.6

Fully covered
(9/10/11) 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. (9/10) limited to linear functions.

Analyze functions using different representations.

F.IF.7

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

F.IF.7a

Partially covered
(9/10) Graph linear, quadratic and absolute value functions and show intercepts, maxima, minima and end behavior.

F.IF.7b

Mostly covered
(11) Graph square root, cube root, and exponential functions.

F.IF.7c

Not covered
(11) Graph logarithmic functions, emphasizing the inverse relationship with exponentials and showing intercepts and end behavior.
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F.IF.7d

Fully covered
(+) Graph piecewise-defined functions, including step functions.

F.IF.7e

Fully covered
(11) Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F.IF.7f

Fully covered
(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

F.IF.7g

Fully covered
(+) Graph trigonometric functions, showing period, midline, and amplitude.

F.IF.8

Write a function in different but equivalent forms to reveal and explain different properties of the function.

F.IF.8a

Fully covered
(9/10) Use different forms of linear functions, such as slope-intercept, standard, and point-slope form to show rate of change and intercepts.

F.IF.8b

Fully covered
(11) Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F.IF.8c

Fully covered
(11) Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = 91.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay.

F.IF.9

Fully covered
(all) Compare properties of two functions using a variety of representations (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, a quantity increasing exponentially eventually exceeds a quantity increasing linearly.