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STANDARDS

Math

Common Core Math

High School: Functions: Interpreting Functions

HSF.IF.A

Understand the concept of a function and use function notation.

HSF.IF.A.1

Fully covered
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).

HSF.IF.A.2

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

HSF.IF.A.3

Mostly covered
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

HSF.IF.B

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

HSF.IF.B.4

Partially covered
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.

HSF.IF.B.5

Fully covered
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

HSF.IF.B.6

Fully covered
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.

HSF.IF.C

Analyze functions using different representations.

HSF.IF.C.7

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

HSF.IF.C.7.a

Partially covered
Graph linear and quadratic functions and show intercepts, maxima, and minima.

HSF.IF.C.7.b

Mostly covered
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

HSF.IF.C.7.c

Fully covered
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
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HSF.IF.C.7.d

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

HSF.IF.C.7.e

Mostly covered
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

HSF.IF.C.8

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

HSF.IF.C.8.a

Fully covered
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.

HSF.IF.C.8.b

Fully covered
Use the properties of exponents to interpret expressions for exponential functions.

HSF.IF.C.9

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