Determine the equation of the horizontal asymptotes, if any, of the function.
f(x)=(2x+1)/(x+1)

Question

Determine the equation of the horizontal asymptotes, if any, of the function.
f(x)=(2x+1)/(x+1)

haleyelizabeth2017 · Answer

$$f(x)=\frac{ 2x+1 }{ x+1 }$$

rizags · Answer

are you allowed to use limits?

haleyelizabeth2017 · Answer

I'm not sure.

rizags · Answer

what class is this for?

haleyelizabeth2017 · Answer

PreCalculus

rizags · Answer

ok then maybe some limits are allowed

rizags · Answer

are you familiar with limits?

haleyelizabeth2017 · Answer

Nope.  But...the book gives us two methods we can use.  Solving for x in terms of y is one method, and divide the numerator and denominator by the highest power of x is the second.

rizags · Answer

yes use the second

rizags · Answer

multiply the whole thing by $$\large \frac{\frac{1}{x}}{\frac{1}{x}}$$

anonymous · Answer

the numerator and denominator are both polynomials
the degrees are the same (they are both of degree 1)
the horizontal asymptotes is the ratio of the leading coefficients

anonymous · Answer

in your example it is $$y=\frac{2}{1}=2$$

anonymous · Answer

it always works this way if the degrees are the same
if they are not, then it is different

haleyelizabeth2017 · Answer

Okay, sorry...was afk for a moment there

anonymous · Answer

if the degree of the denominator is larger, then it is $y=0$
if the degree of the numerator is larger, then there is no  horizontal asymptote

haleyelizabeth2017 · Answer

Okay, good to know.  Thank you