This function includes the "absolute value" function. Think: What is the domain of that function? Secondly, what is the range of y=|x-2|? Does f(x) have a lower limit? an upper limit?
Find the range of 5|x-2|. Then find the range of 5|x-2|+4. What effect does adding that 4 have on the range of y=5|x-2|?