Write the equation of a Rational Algebraic Function in f(x) = n(x)/d(x) form that has a vertical asymptote at x=9 and a horizontal asymptote at y=0

Answer 1

f(x) = 1/(x-9)

graphically has asymptotes x=9 and y=0

x never = 9

and

y never = 0

9 and 0 are limits that x and y approach but never reach

f(x) = n(x)/d(x)

with n(x)=1

and

d(x) = x-9

f(x)=y

y= 1/(x-9) is a rectangular hyperbola with 2 separate branches, centered on the origin

one branch in quadant I, the other in quadrants III & IV, vertices: (9,1) and (7,-1)

it's the rectangular hyperbola f(x)=1/x shifted horizontally 9 units to the right

with the vertical asymptote also shifted right 9 units, but the horizontal asymptote stays the same