Many functions actually don't have these asymptotes. For example, every polynomial function of degree at least 1 has no horizontal asymptotes. Instead of leveling off, the y-values simply increase or decrease without bound as x heads further to the left or to the right.
Nope not all the rational functions have a horizontal asymptote
The graph of an exponential function f(x) = bx approaches, but does not cross the x-axis. The x-axis is a horizontal asymptote.
Yes.
The horizontal asymptote is what happens when x really large. To start with get rid of all the variables except the ones with the biggest exponents. When x is really large, they are the only ones that will matter. If the remaining exponents are the same, then the ratio of those coefficients tell you where the horizontal asymptote is. For example if you have 2x3/3x3, then the ratio is 2/3 and the asymptote is f(x)=2/3 or y=2/3. If the exponent in the denominator is bigger, than y=0 is the horizontal asymptote. If the exponent in the numerator is bigger, than there is no horizontal asymptote.
-1
8
Piece wise functions can do everything. Take two pieces of two rational functions, one have a horizontal asymptote as x goes to -infinity and the other have a slanted (oblique) one as x goes to +infinity. It is still a rational function.
The only trig functions i can think of with horizontal assymptotes are the inverse trig functions. and they go assymptotic for everytime the non-inverse function is equal to zero.
An asymptote is the tendency of a function to approach infinity as one of its variable takes certain values. For example, the function y = ex has a horizontal asymptote at y = 0 because when x takes extremely big, negative values, y approaches a fixed value : 0. Asymptotes are related to limits.
I don't know, what?
The horizontal asymptote for y = 0 when the degree is greater than the denominator, resulting in the inability to do long division.
2x-2/x^2+3x-4