Answer:However, we need to consider that the range can also be affected by the transformation 2x. Since the x-values are multiplied by 2, the y-values will also be compressed horizontally. This means that the range of the translated function will be compressed by a factor of 2. So, the final range of the translated function is {0<=y<=10}/2, which simplifies to {0<=y<=5}. However, we added 3 to the translated function, which shifts the range upwards. So, the final range of the translated function y=f(2x)+3 is {0+3<=y+3<=5+3}, which simplifies to {3<=y<=8}.