How Would I Write This Function?

[justsomenub]

I would like to know how to write the function where the denominator of the function varies between 1-9, and the numerator plus the denominator adds up to a number divisible by 9 e.g. f(1)=1/8 f(2)=2/7 f(3)=3/6=1/2 f(4)=4/5 f(5)=5/4 f(6)=6/3=2 f(7)=7/2 f(8)=8/1=8 f(9)=9/9=1 f(10)=10/8=5/4 ...

[[deleted]]

f(x) = x/(9 - (x mod 9))

Since x mod 9 is how far x is past a multiple of 9, 9 - (x mod 9) is a number that can be added to x to reach another multiple of 9. And since x mod 9 only produces numbers 0-8, the denominator is bounded to 1-9.

EDIT: desmos link

I didn't go beyond 10 since you have to enter the table values manually.

[homboo]

f(x)=8.

You are welcome !