Determine the vertical asymptotes of the following functions

Determine the vertical asymptote(s) of the following functions. Separate multiple answers with a comma. If there is no vertical asymptote write DNE. a. f(x) = x + 6/x^2 + 1 x = b. g(x) = 4/x^2 + 12x + 35 x = c. h(x) = x^2 -3/x^2 -1 x = d. p(x) = 12x^2 + 13/x^2 - 5x + 4 x =

Solution

Solution:

(a)

Vertical asymptotes are the zeros of denominator of f(x)

ie x^2 +1 =0

and we can see that no real any real solution

therefore VA is DNE

(b)

Vertical asymptotes are the zeros of denominator of f(x)

ie x^2 +12x+35 =0

(x+5) (x+7) = 0

x = -5 and x = -7

and we can see that x= -5 and x=-7 are VA

therefore -5,-7 are VA

(c)

Vertical asymptotes are the zeros of denominator of f(x)

ie x^2 -1 =0

(x-1) (x+1) = 0

x = 1 and x = -1

and we can see that x= -1 and x= 1 are VA

therefore -1, 1 are VA

(d)

Vertical asymptotes are the zeros of denominator of f(x)

ie x^2 -5x+4 =0

(x-1) (x-4) = 0

x = 1 and x = 4

and we can see that x= 1 and x= 4 are VA

therefore 1,4 are VA