If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

STANDARDS

 > 

US-ND

Math

North Dakota Math

High School—Functions: Interpreting Functions

Understand the concept of a function and use function notation

HS.F-IF.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).

HS.F-IF.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.

HS.F-IF.3

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

Interpret functions that arise in applications in terms of the context

HS.F-IF.4

Partially covered
Use tables, graphs, verbal descriptions, and equations to interpret and sketch the key features of a function modeling the relationship between two quantities.

HS.F-IF.5

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

HS.F-IF.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.

Analyze functions using different representations

HS.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.

HS.F-IF.7.a

Mostly covered
Graph linear and quadratic functions and show intercepts, maxima, and minima where appropriate.

HS.F-IF.7.b

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

HS.F-IF.7.c

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

HS.F-IF.7.d

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

HS.F-IF.7.e

Mostly covered
Graph exponential and logarithmic functions, showing intercepts and end behavior.

HS.F-IF.7.f

Fully covered
Graph f(x) = sin x and f(x) = cos x as representations of periodic phenomena.

HS.F-IF.7.g

Not covered
(+) Graph trigonometric functions, showing period, midline, phase shift and amplitude.
(Content unavailable)

HS.F-IF.8

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

HS.F-IF.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.

HS.F-IF.8.b

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

HS.F-IF.9

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