Question 290199
{{{ y=(x^2+4x)/(x^3-2x^2-x+2) }}}
{{{ y=(x*(x+4))/((x-2) (x-1) (x+1)) }}}
             

The degree on the denominator (namely, 3) was bigger than the degree on the numerator (namely, 2), and the horizontal asymptote was y = 0 (the x-axis). This property is always true: If the degree on x in the denominator is larger than the degree on x in the numerator, then the denominator, being "stronger", pulls the fraction down to the x-axis when x gets big. That is, if the polynomial in the denominator has a bigger leading exponent than the polynomial in the numerator, then the graph trails along the x-axis at the far right and the far left of the graph.