Exponentials: Transformations

Exponentials

Transformations

The transformations of functions that were presented in the Families of Functions unit also apply to exponential functions. The following list shows how the patterns apply to exponentials:

1. y = 2 ^x + a translates the graph a units up; asymptote equation y = a

2. y = 2 ^x-a translates the graph a units down; asymptote equation y = -a

3. y = 2 ^x-atranslates the graph a units right; asymptote equation y = 0

4. y = 2 ^x+atranslates the graph a units left; asymptote equation y = 0

5. y=-(2 ^x) reflects the graph across the x-axis; asymptote equation y = 0

6. y = 2 ^-x reflects the graph across the y-axis; asymptote equation y = 0