## haleyelizabeth2017 one year ago Determine the equation of the horizontal asymptotes, if any, of the function. f(x)=(2x+1)/(x+1)

1. haleyelizabeth2017

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

2. Rizags

are you allowed to use limits?

3. haleyelizabeth2017

I'm not sure.

4. Rizags

what class is this for?

5. haleyelizabeth2017

PreCalculus

6. Rizags

ok then maybe some limits are allowed

7. Rizags

are you familiar with limits?

8. haleyelizabeth2017

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.

9. Rizags

yes use the second

10. Rizags

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

11. anonymous

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

12. anonymous

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

13. anonymous

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

14. haleyelizabeth2017

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

15. anonymous

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

16. haleyelizabeth2017

Okay, good to know. Thank you