Sec. 2.3 – Stretching, Shrinking, and Reflecting Graphs
Stretching/Shrinking
multiplying
or
dividing
by a value
See class handout!!
Ex. f(x) =  x 
g(x) = 3  x 
we are multiplying the basic graph by 3 (and the
3 is
outside
the absolute value operation), this
will multiply the yvalue of each point by 3 or stretch the graph
vertically
FROM
THE XAXIS
by a factor of 3!!
Ex. f(x) =
1
3
x
or
3
x
Here we are dividing the ycoordinate of each point by 3!
Which will “contract” (“shrink”) the graph vertically
towards
the
xaxis
.
Outside change :
2
( )
f x
x
=
and
2
( )
3
g x
x
=
. Since the 3 is
outside
the
squaring operation, this will
stretch
the graph
vertically
by a factor of
3
from the xaxis
.
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Inside change :
2
( )
f x
x
=
and
2
( )
(3 )
g x
x
=
. Since the 3 is
inside
the
squaring operation, this will affect the graph
horizontally
and the affect
will be the
opposite
of multiplying by 3, i.e. it will contract the graph
horizontally by a factor of 3 towards the yaxis. (Horizontal changes
work “’backwards”! Vertical changes work “normally”’!)
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 Spring '10
 stean
 Multiplication, Continuous function, Complex number, Elementary mathematics

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