Transformation: Vertical stretch by a factor of 6, a horizontal translation 5 units to the left and a vertical translation 2 units down. Graph:
Practice makes perfect
We want to graph the given exponential function as a transformation of its parent function.
g(x)= 6(1/2)^(x+ 5)- 2
Looking at the function, we can see that it has been stretched by a factor of 6, translated 5 units to the left and translated 2 units down.
Let's show the transformations one at a time.
Vertical Stretch
Let's start by considering the parent function f(x)=( 12)^x. If we multiply ( 12)^x by 6, we obtain a vertical stretch by a factor of 6. The resulting function is y=6( 12)^x.
Horizontal Translation
Now, we need to consider the function y=6( 12)^(x+5). This is a horizontal translation of y=6( 12)^x to the left by 5 units.
Vertical Translation
Finally, we will consider the function g(x)=6( 12)^(x+5)-2. This is a vertical translation of y=6( 12)^(x+5) down by 2 units.
Extra
Possible Transformations
The following table illustrates the general form for all possible transformations of functions.
