A) The student will determine whether a given relation is a function.
B) The student will determine the domain and range of a function.
A relation is any set of ordered pairs (x,y). There may be more than one y-value for each x-value.
A function is a type of relation where each x-value only has 1 y-value (x-values don't repeat):
Example:
If a relation is {(2,3),(3,4)} then it is a function because the x-values don't repeat.
If a relation is {(2,3),(2,4)} then it is not a function because the x-values repeat ("2" occurs more than once).
Some relations are functions; all functions are relations.
When reading a table of x-values (inputs) and y-values (outputs), a function cannot have multiple outputs for a given input. Basically, the x-values cannot repeat.
As a set of ordered pairs, a function has a unique or different y-value assigned to each x-value.
Example:
The set of ordered pairs, {(1, 2), (2, 4), (3, 2), (4, 8)} is a function.
This set of ordered pairs, {(1, 2), (2, 4), (3, 2), (2, 3)}, is not a function because the x-value of “2” has two different y-values (4 and 3).
Graphs of functions can be discrete (separate, or individual, points) or continuous (a line). If the graph is discrete (separate points), then the space between the points doesn't matter and is ignored.
Example: the number of pets in a home is a discrete function because you don't have fractions of a pet.
Vertical Line Test: the graph of a function must pass the vertical (up & down) line test. When looking at a graph, the vertical line cannot touch 2 points on the graph at the same time. If this happens, then the graph is not a function.
Functions may be represented as ordered pairs, tables, graphs, equations, physical models, or in words. Any given relationship can be represented using multiple representations.
You should be able to make connections between the different representations of a function.
The domain is the set of all the x-values. This is also referred to as the input or the independent variable.
The range is the set of all the y-values. This is also referred to as the output or dependent variable.
If a function is comprised of a discrete set of ordered pairs (individual points), then the domain is the set of all the x-coordinates, and the range is the set of all the y-coordinates. These sets of values can be determined given the different representations of the function (e.g., ordered pairs, tables, graphs, equations, physical models, or words).
LIFE HACK: DIXI RDYO (Dixie Rodeo)
Domain
Independent Variable
X-values
Input
Range
Dependent Variable
Y-values
Output
Determine whether a relation is a function. Relations can be represented by a set of ordered pairs, a table, or a graph of discrete points. Sets are limited to no more than 10 ordered pairs. (a)
Identify the domain and range of a function represented as a set of ordered pairs, a table, or a graph of discrete points. (b)
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