Question

A rational function of the form y = a/(x - h) + k has asymptotes at x = 4 and y = - 2.
Write the equations of two different functions that meet this description.

I am completely blank on this! Please help.

Answer 1

in your equation y = a/(x - h) + k
a vertical asymptote is caused by the x-h, it can't be zero
so the h must be 4
a horizontal asymptote is caused when the term a/(x-4) gets closer and closer to zero
then you would be left with y = 0 + k
so k = -2

your equation could be y = a/(x-4) - 2

we know nothing about a, so it could be anything
e.g.
y = 3/(x-4) - 2
y = -5/(x-4) - 2

notice in the graphs shown, both have x=4 as a vertical asymptote and
y = -2 as a horizontal asymptote

btw, if a = 0 , we would get the horizontal line of y = -2 with a hole at (4,-2)