MATHEMATICS STANDARDS
GRADES 68
MATH GRADE 8: FUNCTIONS
FUNCTIONS


By the end of Grade
8

Students grasp the concept of a function as a
rule that assigns to each input exactly one output. They understand that
functions describe situations where one quantity determines another. They can
translate among representations and partial representations of functions
(noting that tabular and graphical representations may be partial
representations), and they describe how aspects of the function are reflected
in the different representations.


Define,
evaluate, and compare functions.

RESOURCES


8F.A.1

Understand that a function is a rule that
assigns to each input exactly one output. The graph of a function is the set
of ordered pairs consisting of an input and the corresponding output.


8F.A.2

Compare
properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal
descriptions). For example, given a linear function represented by a table of
values and a linear function represented by an algebraic expression,
determine which function has the greater rate of change.


8F.A.3

Interpret
the equation y = mx + b as defining a linear function, whose graph is a
straight line; give examples of functions that are not linear. For example,
the function A = s2 giving the area of a square as a function of its side
length is not linear because its graph contains the points (1,1), (2,4) and
(3,9), which are not on a straight line.


Use
functions to model relationships between quantities.

RESOURCES


8F.A.4

Construct
a function to model a linear relationship between two quantities. Determine
the rate of change and initial value of the function from a description of a
relationship or from two (x, y) values, including reading these from a table
or from a graph. Interpret the rate of change and initial value of a linear
function in terms of the situation it models, and in terms of its graph or a
table of values.


8F.A.5

Describe
qualitatively the functional relationship between two quantities by analyzing
a graph (e.g., where the function is increasing or decreasing, linear or
nonlinear). Sketch a graph that exhibits the qualitative features of a
function that has been described verbally.

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