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+1

1) Vertical asymptote is x=0

2) f (x) = 2 / (x² + 3x - 10) = 2 / [ (x + 5) (x - 2) ]

Vertical asymptotes are x=2 and x=-5.

3) It's a linear function, just a line, with a slope of 4/7 and a y-intercept of 0 because b=0. the degree of the numerator is 1 and the degree of the denominator is 0. 1>0 so we do not have any horizontal asymptotes.

4) y = (7x+1) / (2x-9)

2xy - 9y = 7x + 1

2xy - 7x = 9y+1

x = (9y + 1) / (2y - 7)

y=7/2

5)

6), y=x-6 is your oblique asymptote

7) line y=2x - 3

8) There is a horizontal asymptote and two vertical asymptotes though.

They are y=0, x = 13, andx = - 2

9) The oblique or slant asymptote is 4x-5.