Answer:
The values of x are -6 , 0 , 1 ⇒ Answers C , D , E
Step-by-step explanation:
* Let revise how to find the vertical asymptote
- Vertical asymptotes of a rational function f(x)/g(x) can be found by
solving the equation g(x) = 0 ⇒ the denominator of the fraction
- Note: this only applies if the numerator f(x) is not zero for the same
x value
* Lets solve the problem
∵ F(x) = 1/x(x + 6)(x - 1)
∵ The denominator of the fraction is x(x + 6)(x - 1)
- To find the equation of the vertical asymptote Put the
denominator = 0
∴ x(x + 6)(x - 1) = 0
- The denominator has three factors, equate each by 0
∴ x = 0
OR
∴ x + 6 = 0 ⇒ subtract 6 from both sides
∴ x = -6
OR
x - 1 = 0 ⇒ add 1 to both sides
∴ x = 1
∴ From all above there are 3 vertical asymptotes at x = -6 , 0 , 1
* The answers are C, D , E
