Question

What are the vertical asymptotes, horizontal asymptotes, slant asymptotes, and the holes of this equation:

(x^2-9x+20)/(2x^2-8x)

Answer 1

asymptotes occur where the function is undefined, in this case your denominator cannot = 0, because that would cause it to be undefined, so if we set, 2x^2-8x = 0, 2x(x-4)= 0, so x cannot = 0 and x cannot = 4. These will be vertical asymptotes because they are defined explicity for x=0, and x=4. Otherwise the function is continuous.

Answer 2

ok thank you. but what are the slant asymptotes and holes of the equation?

Answer 3

slant asymptotes are where you have a line eq as an asyptote, hyperbolas are the best example of that, and holes uusally occur when you have some sort piecewise function that tells you the equation is valid for a values except one. like if f(x) = 2x+5 and f(x) does not exist for x=2, then you have a hole at(2,9)