Find the vertical asymptotes if any of the graph of the rati

Find the vertical asymptote(s), if any, of the graph of the rational function. g(x) = x + 1/x - 7 h(x) = x^2 - 100/(x - 2)(x + 5) f(x) = x^2 + 6x/x^2 - 3x - 54 f(x) = x - 4/x^2 + 9 h(x) = (x - 2)(x + 9)/x^2 - 4 g(x) = x - 2/(x - 2)(x + 6) f(x) = (x - a)(x - b)^3/(x - a)(x - b) Identify any vertical asymptotes in the graph.

Solution

Vertical asymtotes can be found by equating denomiantor to zero and solve for x

1) g(x) = (x+4)/(x-7)

x-7 =0 ; x= 7 (V.A.)

2) f(x) = (x^2- 100)/(x-2)(x+5)

(x-2)(x+5) =0

x= 2 and x = -5 are the V.A.s

3) f(x) = (x^2 +6x)/(x^2 - 3x - 54)

(x^2 - 3x - 54) =0

x^2 -9x +6x -54=0

x(x-9) +6(x -9) =0

(x+6)(x-9) =0

x =-6 and x =9 are V.As

4) f(x) = (x-4)/(x^2 +9)

x^2 +9 = 0 ; x= 3i , -3i

No realsolution so no V.As exist

8) In the graph there are no x intercepts i.e. where graph crosses x axis

so no V.As exist