Question

the vertical and horizontal asymptotes of a reciprocal function are gven below write an equation that could represent the function asymptotes x = 3 and y = -2

Answer 1

One simple choice is
f(x) = 1/(x − 3) − 2.

Reason: f has a vertical asymptote where the denominator is 0 (x = 3), and as x → ±∞ the 1/(x − 3) term → 0 so f → −2 (horizontal asymptote y = −2). More generally any nonzero constant a gives f(x) = a/(x − 3) − 2.