Rational Functions

Question

Write the equation of a possible rational function given the following information.

A) Vertical asymptotes x=-1,2 and x-intercepts at x=-3 and x=4

B) vertical asymptote x=2, discontinuous point (-2,-3/4) and x-intercepts at x=-5

Answer 1

A) y= (x+3)(x-4)/(x-2)(x+1)

B) y = (x+5)/(x-2) ignoring the discontinuity

with the discontinuity

y = (x+5)(x+2)/(x-2)(x+2) which changes nothing, as the x+2 factors cancel, other than remove -2 as a point on the graph. Still it has to be a point on the curve to be a discontinuity. so the graph has to have had (-2,-3/4) as a point otherwise.

plug that point into the first equation

-3/4 = (-2+5)/(-2-2) = 3/-4. It's true, so it works. that's the equation you want

y=(x+5)(x+2)/(x-2)(x+2) or if you prefer multiply it out

y= (x^2 +7x +10)/(x^2 -4)