SOLUTION: Problem: f(x) = (3x -1)/ (x + 4)= Domain (- infinity, -4) u (-4, infinity) Find the equations of both vertical and horizontal asymptotes of the function. Please show work or

Algebra ->  Functions -> SOLUTION: Problem: f(x) = (3x -1)/ (x + 4)= Domain (- infinity, -4) u (-4, infinity) Find the equations of both vertical and horizontal asymptotes of the function. Please show work or       Log On


   

Question 451874: Problem: f(x) = (3x -1)/ (x + 4)= Domain (- infinity, -4) u (-4, infinity)
Find the equations of both vertical and horizontal asymptotes of the function.
Please show work or explain in Words.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Considering only the highest powers for the numerator and denominator, the function is reduced to %283x%29%2Fx+=+3. Letting x approach infinity, f(x) then approaches 3, and hence the horizontal asymptote is y = 3.
The vertical asymptote is where x + 4 = 0, or x = -4, which is the equation of the vertical asymptote itself.