Question

Which function has vertical asymptotes at x=-1 and x=-2, an x-intercept at(8,0) , and no holes?

Answer 1

y = (x - 8)/((x + 1)(x + 2))

Explanation:

vertical asymptotes are given as at x=-1 and x=-2

Now, vertical assymptotes are values of x when the denominator is zero.

Thus, the function of the denominator can be written as;

(x + 1)(x + 2)

We are also told that x-intercept at (8,0).

Which means that y is zero when x is 8.

Thus, numerator is 8 when y is zero.

Thus, numerator can be expressed as (x - 8)

Thus,the function is now;

y = (x - 8)/((x + 1)(x + 2))