Originally Posted by
nzmathman Ok, we have 1 horizontal asymptote and 1 vertical asymptote, so this is a rectangular hyperbola, in the form:
$\displaystyle (y - b) = \frac{c}{x - a}$
The asymptotes, and thus the function, have shifted up 21 (=b) and shifted left -7 (=a).
Thus,
$\displaystyle
(y - 21) = \frac{c}{x + 7}$
To find c, simply substitute in a known coordinate: (6,0) or (0,-18).
Substituting in (6,0), we get
$\displaystyle
(0 - 21) = \frac{c}{6 + 7}$
$\displaystyle
-21 = \frac{c}{13}$
$\displaystyle c = -21 \times 13 = -273$
Thus the equation is:
$\displaystyle
(y - 21) = \frac{-273}{x + 7}$