Answer:
Dilation followed by Translation.
Step-by-step explanation:
We have the function .
The new transformed function is
Now, the transformation applied to f(x) to obtain g(x) are:
1. Dilation - it is the transformation that changes the size/shape of the figure. It is generally of the form kf(x) where k is constant.
Since, we are dilating the given function by 2 units, the new dilated function becomes .
2. Translation - it is the transformation that shifts the figure in any direction. When the function is shifted vertically, the general form becomes f(x)+k.
As, we see that the new dilated function is shifted 3 units upwards, the final translated function becomes .
Hence, the transformations applied to obtain g(x) from f(x) are Dilation followed by Translation.