Question

1. Identify the vertical asymptotes of

Answer 1

1. x1/2=$\frac{-3\pm \sqrt{9+40} }{2}$
VA(the vertical asymptotes): x=-5,  x=2
2. x1/2=$\frac{9\pm \sqrt{81-72} }{2}$
VA: x=3, x=6
3.  $\lim_{n \to \infty} \frac{4x}{7}$=∞
There is no HA.
4. $\lim_{n \to \infty} \frac{7x+1}{2x-9}= \frac{7}{9}$
HA : y=7/2
5. $\lim_{n \to \infty} \frac{ x^{2} +5x+3}{4x-1}$ =∞
There is no HA.
6. m=$\lim_{n \to \infty} \frac{ x^{2} -4x+8}{ x^{2} +2x}$
m = 1
b=$\lim_{n \to \infty} \frac{ x^{2} -4x+8- x^{2} -2x}{x+2}$
b = -6
OA: y = x - 6
7. Same method:
m = 2
b = 0
OA: y = 2x
8. m = 0
There is no OA.
m = 4 
b=-1
OA: y=4x-1