Let f(x)=[(x-8)(x+7)] / [(9x+8)(8-x)]
What is the vertical asymptote and the horizontal asymptote?
I know that the vertical asymptote is supposed to be the zeroes of the denominator but it didn"t really work out. I also tried plugging in very large numbers to find the horizontal asymptote with no success.

Question

Let f(x)=[(x-8)(x+7)] / [(9x+8)(8-x)]
What is the vertical asymptote and the horizontal asymptote?
I know that the vertical asymptote is supposed to be the zeroes of the denominator but it didn"t really work out.  I also tried plugging in very large numbers to find the horizontal asymptote with no success.

anonymous · Answer

okay, while it is true that vertical asymptotes occur at values of x that make the denominator zero, if you can cancel the term in the denominator with a term in the numerator, it is a hole instead

so your current equation, can be written like so

$$f(x) = \frac{ (x-8)(x+7) }{ (9x+8)(8-x) } = \frac{ -1(8-x)(x+7) }{ (9x+8)(8-x) }$$ 

so there is a hole at x = 8, and a vertical asymptote for the x value where 9x+8 = 0

after you simplify the equation you can try determining the horizontal asymptote again

anonymous · Answer

Well I thought that the vertical would be $$-\frac{ 8 }{ 9 }$$ but I cannot put fractions and I already tried putting it in as -8/9.  When I plug in large numbers for the horizontal I am getting about -0.11, does that seem correct?

anonymous · Answer

yup those are correct