Question

For the following function find the vertical, horizontal, and oblique asymptotes, if any. Please show all of your work. f(x) = 4x/7x^2+6x-16 +25 For the following function find the vertical, horizontal, and oblique asymptotes, if any. Please show all of your work. f(x) = 4x/7x^2+6x-16 +25 @Mathematics

Answer 1

to find the VA you must make the denominator = 0
\[7x^2+6x-16\]
factor to find the zeros
(7x-8)(x+2)=0
VA are where this equation = 0
8/7, -2

to find the HA you have to find the limit as\[\lim_{x \rightarrow \infty}(4x \div(7x^2+6x-16))+25\]
you divide both top and bottom by the highest degree in the denominator which is x^2