How many numbers are in the range of the function $f(x) = \frac{\lceil 5x - 5\lfloor x \rfloor \rceil}5$?
+128475 Let's pick a few values and see what happens
x= 1....ceiling [ 5 (1) - 5 floor (1) ] / 5 = ceiling [ 5 - 5 ] / 5 = ceiling 0 = 0
x =1.2.....ceiling [ 5(1.2) - 5 floor (1.2) ] /5 = ceiling [ 6 - 5 ] / 5 = 1/5
x = 1.4 .....ceiling [ 5 (1.4) -5 floor (1.4) ] / 5 = ceiling [ 7 - 5(1) ]/ 5 = 2/5
x = 1.6 .....ceiling [ 5 (1.6 ) - 5floor (1.6) ] / 5 = ceiling [ 8 - 5 ] /5 = 3/5
x =1.8.....ceiling [ 5 (1.8) - 5 floor (1.8) ] /5 = ceiling [ 9 - 5] /5 = 4/5
x = 1.9.....ceiling [ 5 (1.9) - 5 floor (1.9] / 5 = ceiling [ 9.5 - 5 ] / 5 = ceiling (4.5) /5 = 5/5 =1
And look at the graph here : https://www.desmos.com/calculator/ixgipsfctk
It appears that this patern is repeated infinitely between integers
So....there are 6 numbers in the range of this function
0, 1/5 , 2/5 , 3/5 , 4/5 and 1
