What is the rational equation?

Question

Vertical Asymptotes x=-3 x=4

Horizontal Asymptote y=-3

passes through 5, -3.25

Answer 1

Vertical Asymptotes x=-3 x=4 mean the factors (x + 3)(x - 4) are in the denominator

Horizontal Asymptote y=-3 means take 1/[(x + 3)(x - 4)] and subtract 3 from it:

1/[(x + 3)(x - 4)) - 3

Passes through: (5, -3.25) means add a factor "a" to the numerator then plug in "x = 5" and "y = -3.25" and solve for "a":

y = a/[(x + 3)(x - 4)) - 3

-3.25 = a/[(5 + 3)(5 - 4)) - 3

-0.25 = a/8

a = -2

Therefore: y = -2/[(x + 3)(x - 4)] - 3