Question

f(x)= 4/(x-2)^3

find vertical and horizontal asymptotes

Answer 1

sorry its f(x)=4/(x-2)^3

Answer 2

To find the vertical asymptotes, set the denominator equal to zero and solve for x

Answer 3

(x-2)^3 = 0

x-2 = 0 ... take the cube root of both sides

x = 2

so the vertical asymptote is x = 2

Answer 4

the degree of the numerator (0) is smaller than the degree of the denominator (3)

So this automatically means you have a horizontal asymptote of y = 0

Answer 5

can you show the horizontal asymptote how you figured that out

Answer 6

the general rule is that if the degree of the numerator is less than the degree of the denominator, then the horizontal asymptote will be y = 0

Answer 7

it's basically because the denominator is growing faster than the numerator as x --> infinity

so f(x) --> 0