## anonymous one year ago f(x)= Solve for Vertical and horizontal Asymptote: x^2+2x+1 / 2x^2-x-3

1. freckles

I would factor denominator and numerator (just in case there are common factors amongst the two) first

2. anonymous

Yeah X+1 cancels. I worked out the problem I just want to see if I did it correctly.

3. freckles

ok so that means there is a hole at x=-1 what was the other factor in the denominator?

4. anonymous

2x-3 and x+1 in the numerator

5. anonymous

I got VA: -1 and HA: 3/2

6. freckles

sounds good so you solved 2x-3=0 to get the vertical asymptote though you could probably just say 2x-3=0 but we know teachers like us to solve this for x now the horizontal asymptote is easier; you have the degrees are the same on top and bottom so you just fetch the coefficient of x^2 on top and bottom

7. freckles

(x+1)'s cancel so you do not have a vertical asymptote at x=-1 2x-3=0 will give you the vertical asymptote and I'm not sure how you got that horizontal asymptote

8. freckles

also leave your asymptotes in equation form because asymptotes are suppose to be described by equations not just numbers

9. anonymous

I used the 1st x+1 in the numerator for VA and 2x-3 in the denominator for HA setting them both equal to zero and the denominator is larger so I believe that would make the denominator be HA.

10. freckles

since the degree on top and bottom are both 2 then that means we just take the coefficients of the terms on top and bottom of the x^2 term to find the horizontal asymptote $y=\frac{\color{red}{1}x^2+2x+1}{\color{red}2x^2-x-3}$

11. freckles

the ha is y=1/2 as we said you do not have a va at x=-1 but you have a hole at x=-1 since the (x+1)'s canceled and you had no more (x+1)'s on bottom but you will have a va when 2x-3=0

12. anonymous

Oh I got it, so 3/2 is the Va?

13. freckles

$f(x)=\frac{(x+1)(x+1)}{(x+1)(2x-3)}=\frac{x+2}{2x-3} , x \neq -1 \\ 2x-3=0 \text{ gives } x=\frac{3}{2} \text{ as the vertical asymptote } \\$ don't just write 3/2 an asymptote is described by an equation not a number

14. freckles

oops that x+2 is a type-o should be x+1 in the numerator

15. anonymous

Alright I got it thanks!

16. freckles

np