The graph of y = f(x) has one vertical asymptote, at x= -7 , and a horizontal asymptote at y = 21 . The graph of f crosses the x-axis once, at x = 6 , and the y-axis at y = -18 . Find the simplest possible formula for the rational function.
The graph of y = f(x) has one vertical asymptote, at x= -7 , and a horizontal asymptote at y = 21 . The graph of f crosses the x-axis once, at x = 6 , and the y-axis at y = -18 . Find the simplest possible formula for the rational function.
Ok, we have 1 horizontal asymptote and 1 vertical asymptote, so this is a rectangular hyperbola, in the form:
The asymptotes, and thus the function, have shifted up 21 (=b) and shifted left -7 (=a).
Thus,
To find c, simply substitute in a known coordinate: (6,0) or (0,-18).
Substituting in (6,0), we get
Thus the equation is: