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

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

How are the graphs of , , , , , , , and related to the graph of ? These important ideas from a precalculus course are illustrated using various common functions including , , and . The graphs of these functions can be translated vertically and horizontally to provide many more examples of . The reset button puts a previously translated graph back to its original position.

f(x-a)

b+f(x)

-f(x)

f(-x)

|f(x)|

f(|x|)

1/f(x)

f(1/x)

f(x)

sin(x)

x

e

|x|

g(x)