We want to graph the given exponential function as a transformation of its parent function.
y= 12(5)^(x- 1)+ 4
Looking at the function, we can see that it has been compressed by a factor of 12, translated 1 unit to the right, and translated 4 units up.
Let's show the transformations one at a time.
Compression
Let's start by considering the parent function y=5^x. If we multiply 5^x by 12, we obtain a vertical compression by a factor of 12. The resulting function is y= 12 (5)^x.
Horizontal Translation
Now, we need to consider the function y= 12(5)^(x-1). This is a horizontal translation of y= 12(5)^x to the right by 1 unit.
Vertical Translation
Finally, we will consider the function y= 12(5)^(x-1)+4. This is a vertical translation of y= 12(5)^(x-1) up by 4 units.
Extra
Possible Transformations
The following table illustrates the general form for all possible transformations of functions.
