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Instructions on graphing piecewise defined functions by creating input/output tables for each piece and plotting the ordered pairs. examples of piecewise functions and their corresponding graphs, as well as instructions for setting up tables in LON-CAPA. Students are encouraged to find a minimum of three points for each piece of the function, including endpoints.
What you will learn
Typology: Schemes and Mind Maps
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2
Inputs Outputs
๐
Inputs Outputs
Inputs Outputs
2
Inputs Outputs
๐
Inputs Outputs
Inputs Outputs
Since the first piece
of the function
( 2 ๐ฅ + 3 ) is only
defined for ๐ฅ-values
where ๐ฅ โค โ 2 , its
domain in interval
notation is
(โโ, โ 2 ]. This
means that the
graph of the first
piece will go on
forever in the
negative direction.
The last point that I
plotted for the
graph of the first
piece is (โ 4 , โ 5 ),
but the graph
continues on past
that point since I
could continue to
plug in other ๐ฅ-
values (such as
โ 5 , โ 6 , โ 7 , โฆ).
The graph of the
third piece will also
go on forever, but
in the positive
direction, since its
domain is
( 2 , โ
) .
2
Inputs Outputs
๐
Inputs Outputs
Inputs Outputs
2
2
๐
Inputs Outputs
Inputs Outputs
๐
Inputs Outputs
Keep in mind that
even though the
second piece of the
function ( 2 ๐ฅ + 2 )
has the domain
โ 2 < ๐ฅ โค 2 (which
means that โ 2 is not
part of the domain)
we still need to plug
โ 2 into 2 ๐ฅ + 2 in
order to get the
complete graph of
that piece of the
function. If we
started graphing that
piece of the function
using ๐ฅ = โ 1 as the
first input, weโd be
missing part of the
graph, and the graph
would be incomplete.
So we include
๐ฅ = โ 2 as an input
for the second piece
of the function, but
we plot that point
with an open dot to
indicate that ๐ฅ = โ 2
is not part of the
domain of that piece,
and that the point
(โ 2 , โ 2 ) is not part
of the graph.