Question

1. Identify the vertical asymptotes of

f(x) = 2/x^2+3x-10

2. Identify the vertical asymptotes of f(x) = x+6/x^2-9x +18

3. Identify the horizontal asymptote of f(x) =4x/7

4. Identify the horizontal asymptote of f(x) = 7x+1/2x-9

5.Identify the horizontal asymptote of f(x) = x^2+5x-3/4x-1

6. Identify the oblique asymptote of f(x) = x^2-4x+8 /x+2

7.Identify the oblique asymptote of f(x) = 2x^2+3x+8/x+3

8.Identify the oblique asymptote of f(x) = x+4/3x^2+5x-2

9. Identify the oblique asymptote of
f(x) =4x^2-x+2/x

Answer 1

1. x1/2=
`(-3\pm √(9+40) )/(2)`
VA(the vertical asymptotes): x=-5, x=2
2. x1/2=
`(9\pm √(81-72) )/(2)`
VA: x=3, x=6
3.
`\lim_(n \to \infty) (4x)/(7)`=∞
There is no HA.
4.
`\lim_(n \to \infty) (7x+1)/(2x-9)= (7)/(9)`
HA : y=7/2
5.
`\lim_(n \to \infty) ( x^(2) +5x+3)/(4x-1)` =∞
There is no HA.
6. m=
`\lim_(n \to \infty) ( x^(2) -4x+8)/( x^(2) +2x)`
m = 1
b=
`\lim_(n \to \infty) ( 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