The horizontal asymptote is the value at the y-axis where the graph approaches the line but not necessarily touching it. Hence, the asymptotic characteristic of the graph. The standard form of a function in fraction form is y = (ax^n +...)/(bx^m+...). There are rules to follow to determine the horizontal asymptote of a function. 1) if n = m , then the horizontal equation is y = a/b 2) if n>m, then there is no horizontal equation 3) if n<m, then the horizontal equation is the x axis ; y = 0.
The function given falls on the third rule hence the horizontal asymptote of the function is at y = 0.