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The Effects of Some Simple Compositions on the Graph of a Function

​
f(x)
3
x
-2
2
x
-3x
translate horizontally by a
0
translate vertically by b
0
g(x) = b + f(x - a)
show graph of:
-g(x)
g(-x)
| g(x) |
g( |x| )
1 / g(x)
g(1 / x)
reset f
How are the graphs of
f(x-a)
,
b+f(x)
,
-f(x)
,
f(-x)
,
|f(x)|
,
f(|x|)
,
1/f(x)
, and
f(1/x)
related to the graph of
f(x)
? These important ideas from a precalculus course are illustrated using various common functions including
sin(x)
,
x
e
, and
|x|
. The graphs of these functions can be translated vertically and horizontally to provide many more examples of
g(x)
. The reset button puts a previously translated graph back to its original position.
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