SOLUTION: Given the rational function f(x)=8x-3/ 4x +12 explain in detail how to find the equations of the horizontal and vertical asymptotes. Be sure to conclude your explanation by giving

Algebra ->  Functions -> SOLUTION: Given the rational function f(x)=8x-3/ 4x +12 explain in detail how to find the equations of the horizontal and vertical asymptotes. Be sure to conclude your explanation by giving      Log On


   

Question 688433: Given the rational function f(x)=8x-3/ 4x +12 explain in detail how to find the equations of the horizontal and vertical asymptotes. Be sure to conclude your explanation by giving the equations of the lines for the horizontal
and vertical asymptotes.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
DISCLAIMER: I was never a high math school teacher (just a physics substitute), and do not know the exact answer expected. I just know what makes sense.

I believe f%28x%29=(8x-3)/(4x +12)=%288x-3%29%2F%284x+%2B12%29 is your function.
(Without those brackets we would have f%28x%29=8x-3/ 4x +12 =8x-3%2F+4x+%2B12).
The long horizontal fraction line in f%28x%29=%288x-3%29%2F%284x+%2B12%29 carries those hidden brackets).
f%28x%29=%288x-3%29%2F%284x+%2B12%29 --> f%28x%29=%288x%2B24-3-24%29%2F%284x+%2B12%29 --> f%28x%29=%288x%2B24-27%29%2F%284x+%2B12%29 --> f%28x%29=%288x%2B24%29%2F%284x+%2B12%29-27%2F%284x+%2B12%29 --> f%28x%29=2-27%2F%284%28x%2B3%29%29

As abs%28x%29 grows without bounds, the term -27%2F%284%28x%2B3%29%29 approaches zero, so the value of f%28x%29=2-27%2F%284%28x%2B3%29%29 approaches 2,
making highlight%28y=2%29 the horizontal asymptote.

As x approaches -3, x%2B3 approaches 0 and
abs%28-27%2F%284%28x%2B3%29%29%29 grows without bounds,
making highlight%28x=-3%29 the vertical asymptote.

graph%28300%2C300%2C-18%2C12%2C-8%2C12%2C%288x-3%29%2F%284x+%2B12%29%2C2%29

DISCLAIMER BOOKEND:
Your teacher/textbook may require using certain buzzwords/symbols (e.g. for limits), and/or referencing certain theorems or paint-by-number rules that I cannot guess about.