Start by performing a reflection across the x-axis.
Practice makes perfect
We want to graph the given exponential function as a transformation of its parent function.
y=- 6 ( 34 )^x- 10
Looking at the function, we can see that it has been reflected across the x-axis, stretched by a factor of 6, and translated 10 units down.
Let's show the transformations one at a time.
Reflection
Let's start by considering the parent function y= ( 34 )^x. If we perform a reflection across the x-axis, the resulting function is y=- ( 34 )^x.
Stretch
If we multiply - ( 34 )^x by 6, we obtain a vertical stretch by a factor of 6. The resulting function is y=- 6 ( 34 )^x.
Vertical Translation
Finally, we will consider the function y=- 6 ( 34 )^x-10. This is a vertical translation of y=- 6 ( 34 )^x down by 10 units.
Extra
Possible Transformations
The following table illustrates the general form for all possible transformations of functions.
