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Which statement is true about the discontinuities of the function f(x) x+1/6x^2-7x-3
there are asympotes at x=3/2 and x=-1/3
there are holes at x= 3/2 and x=-1/3
there are asymptotes at x=-3/2 and x= 1/3
there are holes at x=-3/2 and x= 1/3

Respuesta :

meerkat18
we are given with the function f(x)= (x+1)/(6x^2-7x-3) where we are asked in the problem to determine the discontinuities of the functions. In this case, we must find the horizontal asymptotes that is to determine the roots of the function at the denominator. Asymptotes are functions in which they do not necessarily touch the axes, just approaching. Then,

6x^2-7x-3 = 0 
(x-3/2) * (x+1/3) = 0
x=3/2 and x=−1/3
The option applicable in this case is option B. there are holes at x= 3/2 and x=-1/3
lhmarianateixeira

In this exercise we will use the knowledge of functions to identify whether it is a continuous or discontinuous function, like this:

[tex]x=3/2\\x=-1/3[/tex]

Knowing that the given function is:

[tex]f(x)= (x+1)/(6x^2-7x-3)[/tex]

What is asymptotes functions?

Are functions in which they do not necessarily touch the axes, just approaching. In this case, the  horizontal asymptotes is used to determine the roots of the function at the denominator. we have:

[tex]6x^2-7x-3 = 0 \\(x-3/2) * (x+1/3) = 0\\x=3/2\\x=-1/3[/tex]

See more about functions at brainly.com/question/5245372

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