Writing a Rational function

Question

When writing a Rational Function, when I am given the Horizontal Asymptote of y=0 how does that effect my equation compared y=1 or y=-3

Answer 1

When you're writing a rational function, horizontal asymptotes tell you about what happens when x goes to infinity or -infinity. for instance if y=(x+2)/(x²+3x+7), if x is equal to 1,000,000, then we can say the top is pretty much x because 1,000,000+7 is basically just 1,000,000. We can also say the bottom is pretty much just x² because 1,000,000² + 3,000,000 +7 is basically just 1,000,000², so we end up with y=1/1,000,000 which is pretty much 0 and there's a horizontal asymptote at y=0. However, if we had y=(3x+2)/(x-6), when x=1,000,000 the top is pretty much 3x and the bottom is pretty much x, so y=3x/x=3 and we'll have a horizontal asymptote at y=3.