<p>How do you calculate the horizontal and vertical asymptote of a function,
say,
2(x-4)/(x^2-1)</p>
<p>Vertical asymptotes occur where the denominator equals zero.</p>
<p>Horizontal asymptote–it depends. If the denominator is of higher degree than the numerator, then the function will approach the line y=0. If the denominator and numerator are of equal degree, then the function will approach the line y=[the ratio of the lead coefficients]. If the numerator is of higher degree than the denominator, then there will be no horizontal asymptote.</p>
<p>thank you. . . .</p>
<p>While there is no horizontal asymptote if the numerator is of higher degree than the denominator, there is what is called a slant asymptote. Take for example (-3x²+2)/(x-1). You would use long division to figure out that the expression is equal to -3x-3 + (-1/(x-1)). In stating the actual asymptote, you would leave of the remainder, so the slant asymptote for (-3x²+2)/(x-1) is -3x-3.</p>
<p>But only if the degree of the numerator is one greater than the degree of the denominator.</p>
<p>Also, if I see a question about a slant asymptote on a College Board test, I’ll eat my hat.</p>
<p>Sent from my DROIDX using CC App</p>