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Contenido principal

STANDARDS

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US-KY

Math

Kentucky Math

Conceptual Category Functions: Functions—Interpreting Functions

Cluster: Understand the concept of a function and use function notation.

HS.F.1

Understand properties and key features of functions and the different ways functions can be represented. (MP.2, MP.4, MP.7)

HS.F.1.a

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.

HS.F.1.b

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

HS.F.1.c

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.

HS.F.1.d

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

HS.F.1.e

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

HS.F.2

Fully covered
Recognize that arithmetic and geometric sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (MP.7, MP.8)

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

HS.F.3

Understand average rate of change of a function over an interval. (MP.2, MP.4)

HS.F.3.a

Fully covered
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.

HS.F.3.b

Fully covered
Estimate the rate of change from a graph.

Cluster: Analyze functions using different representations.

HS.F.4

Graph functions expressed symbolically and show key features of the graph, with and without using technology (computer, graphing calculator). (MP.4, MP.5)

HS.F.4.a

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

HS.F.4.b

Mostly covered
Graph square root, cube root and absolute value functions.

HS.F.4.c

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

HS.F.4.d

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

HS.F.4.e

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

HS.F.4.f

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

HS.F.4.g

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

HS.F.5

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (MP.3, MP.6)

HS.F.5.a

Mostly covered
Identify zeros, extreme values and symmetry of the graph within the context of a quadratic function.

HS.F.5.b

Fully covered
Use the properties of exponents to interpret expressions for exponential functions and classify the exponential function as representing growth or decay.