Question

Select all the lines below that are an asymptote to the rational function of f(x)= 2x+1/x-9. Picture attached, 15 points and I'll give Brainliest! Due in two hours.

Answer 1

Answer:

Solution : Option A and Option C

Step-by-step explanation:

To determine our vertical asymptote here we can make the denominator of the rational function equivalent to zero ...

x - 9 = 0,

x = 9 - this is our vertical asymptote

Now there are three rules that we need to apply when determining the horizontal asymptote. To do so we take the degree of each " x " term and compare the numerator and denominator degree.

If the numerator (degree) < denominator (degree), we take the degree of the numerator as the asymptote --- (1). If the numerator (degree) = denominator (degree) we take the coefficient of the x terms, and divide --- (2). If the numerator (degree) > denominator (degree) their will be no asymptote.

In this case our degree for the numerator is 1, (x¹) and our degree for the denominator is the same, 1 (x¹). Therefore we divide the coefficients, 2 / 1 = 2. Our horizontal asymptote is y = 2.