Graph and its slant asymptote on the same set of axes.

Question

Graph  and its slant asymptote on the same set of axes.

Quizplus · Accepted Answer

The given rational function has a vertical asymptote at x=3, a horizontal asymptote at y=0 and a slant asymptote y=x/2. To graph both the slant asymptote and the function, we can divide the numerator polynomial by the denominator using polynomial long division. The result will be the slant asymptote plus a remainder whose degree is less than the degree of the denominator. The quotient is y=(x-3)/2, so the slant asymptote is y=x/2 - 3/2. The remainder is (-5x+13)/(x-3), which can be graphed separately. Therefore, option B is the correct choice.

Graph and Its Slant Asymptote on the Same Set