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Sec. 2.2 – Vertical and Horizontal Shifts of Graphs
Transformation of functions
?
“transform” means to change! Ex. A transformer out on
the utility pole. The “transformer” toys you used to get in your Happy Meals would
change from a semitruck into a robot figure.
A
vertical
translation or shift in a functions graph will occur if you add or subtract a
value to the basic function as follows :
f(x) + a
, a>0
will cause the graph to shift up a units. Ex. f(x) = x
g(x) = x + 3
f(x)
 a
, a>0
will cause the graph to shift down a units
h(x) = x  2
A
horizontal
translation or shift in a functions graph will occur if you add or subtract a
value to the basic function as follows :
f(x + a)
, a>0
will cause the graph to shift left a units. Ex. f(x) = x
g(x) = x + 3
f(x
 a)
, a>0
will cause the graph to shift right a units
h(x) = x – 2
Combinations :
f(x + a) + b
shift left a units, and up b units, or reverse order also
f(x – a) + b
shift right a units, and up b units, “
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 Spring '10
 stean

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