Question

At which values of x does the function F(x) have a vertical asymptote? Check all that apply. F(x)=2/3x(x-1)(x 5).

Answer 1

The function F(x) have a vertical asymptote at x =0 and x =1.

Given that

The given Function;

$\rm F(x)=\dfrac{2}{3x(x-1)(x^ 5)}$

We have to determine

At which value the function F(x) has a vertical asymptote.

According to the question

The given Function;

$\rm F(x)=\dfrac{2}{3x(x-1)(x^ 5)}$

The function is undefined when the denominator becomes 0. Find values of x for which the denominator is 0:

Then,

$\rm 3x (x-1) (x^5)= 0$

$\rm x^5 =0, \ \ x=0\\\\ x-1 = 0, \ \ x =1$

The value of x is 0 and 1.

Hence, the function F(x) have a vertical asymptote at x =0 and x =1.

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