3 part differentiation and curve property question

Calculus
Tutor: None Selected Time limit: 1 Day

Consider the function  f(x) = (4x+7) / (6x+3)

For this function there are two important intervals: 

(-inf,A) and (A,inf) where the function is not defined at A

1) Find A:

2) Find the horizontal asymptote of f(x)

3) Find the vertical asymptote of f(x)


Apr 8th, 2015

The function is not defined for 6 x + 3 = 0, that is, at x = -1/2.

1) A = - 1/2

2) Since lim_{x -> infty} f(x) = 4/6 = 2/3, the horizontal asymptote is y = 2/3.

3) The vertical asymptote is x = 2/3 because lim_{x -> -1/2+0} f(x) = + infty and  lim_{x -> -1/2-0} f(x) = - infty.

Apr 8th, 2015

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Apr 8th, 2015
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