Question

What are the steps necessary to write a function? Example,
Create a function that has a removable discontinuity at x = b, a horizontal asymptote at "a", and a y-intercept at "c".
I have a gap between math classes and I know I'm missing something here.
I can't find the information necessary to build my function.

Answer 1

0/0 is undefined, but it produces a removable discontinuity.
So, y = (x-b)/x-b) has a removable discontinuity at x=b.

h/0 is undefined, and produces an asymptote at x=h, so
y = (x-b) / ((x-b)(x-a))
works for the 2nd criterion

0/h = 0 for any h not zero, so your final function will look like

y = (x-b)(x-c) / (x-b)(x-a)
If you define y(b) = (b-c)/(c-a) then that takes care of the removable discontinuity. So make sure that c≠a, or you will have another asymotote.