At which values of x does the function F(x) have a vertical asymptote? Check all that apply.𝐹(𝑥)=72𝑥(𝑥+3)(𝑥−9)F(x)= 2x(x+3)(x−9)7 A.-9B.9C.0D.7E.-3F.3SUBMITarrow_backPREVIOUS
Question
At which values of x does the function F(x) have a vertical asymptote? Check all that apply.𝐹(𝑥)=72𝑥(𝑥+3)(𝑥−9)F(x)= 2x(x+3)(x−9)7 A.-9B.9C.0D.7E.-3F.3SUBMITarrow_backPREVIOUS
Solution
A function has a vertical asymptote at the values of x for which the function is undefined. For the function F(x) = 2x(x+3)(x-9)/7, the function is undefined when the denominator is zero. However, in this case, the denominator is a constant (7), which is never zero. Therefore, we need to look at the numerator of the function.
The numerator of the function is zero when x = 0, x = -3, or x = 9. However, these are not vertical asymptotes, but rather the x-intercepts of the function.
Therefore, the function F(x) = 2x(x+3)(x-9)/7 does not have any vertical asymptotes. So, none of the options A.-9, B.9, C.0, D.7, E.-3, F.3 are correct.
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