Question

How to find vertical ad horizontal asymptotes f(x)=8/3x-6

a) Factorize the numerator
b) Factorize the denominator
c) Set the denominator equal to zero
d) Set the numerator equal to zero

Answer 1

To find the vertical and horizontal asymptotes of f(x) = 8/(3x - 6), you need to factorize the numerator and denominator separately. There is no horizontal asymptote, but the vertical asymptote is x = 2.

Step-by-step explanation:

1. Factorize the numerator: The numerator is already in its simplest form, so it cannot be further factorized.
2. Factorize the denominator: The denominator is in the form of 3x - 6, which can be factored out to 3(x - 2).
3. Set the denominator equal to zero: 3(x - 2) = 0
4. Set the numerator equal to zero: 8 = 0 (This is not possible since 8 will never equal zero)

Since the numerator does not equal zero, there is no horizontal asymptote. The denominator, 3(x - 2), will equal zero when x = 2. Therefore, the vertical asymptote is x = 2.