Question

help with some asymptotes of rational functions?

Answer 1

@ranga please!

Answer 2

@SolomonZelman

Answer 3

1) Vertical lines have the equation x = constant because all points on the vertical line will have the same x value. In diagram 1 you can see the vertical asymptote is at x = 12.

For 2) you get a vertical asymptote at x values that makes the denominator zero. So we need to find when x^2 - 7x - 30 equals zero. Solve for:
x^2 - 7x - 30 = 0
Factor the left hand side:
x^2 - 10x + 3x - 30 = 0
x(x - 10) + 3(x - 10) = 0
(x - 10)(x + 3) = 0
x = 10 or -3. These two x values will make the denominator go to zero and will make the function go to infinity. Therefore, x = 10 and x = -3 are the vertical asymptotes.