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jek_recluse [69]
3 years ago
14

What are the vertical and horizontal asymptotes for the function f (x) = StartFraction x squared + x minus 6 Over x cubed minus

1 EndFraction?
Mathematics
1 answer:
Lelu [443]3 years ago
7 0

<u>Given</u>:

The given function is f(x)=\frac{x^{2}+x-6}{x^{3}-1}

We need to determine the horizontal and vertical asymptote.

<u>Horizontal asymptote:</u>

From the given function, it is obvious that the denominator's degree is greater than the numerator's degree.

Then, the horizontal asymptote is the x - axis.

Thus, the horizontal asymptote is y=0

<u>Vertical asymptote:</u>

The vertical asymptote of the rational function are the undefined points and can be determined by equating the denominator equal to zero.

Thus, we have;

x^3-1=0

     x^3=1

Solving, we get;

x=1, x=\frac{-1+\sqrt{3} i}{2}, x=\frac{-1-\sqrt{3} i}{2}

Thus, the function is undefined at the point x=1

Hence, the vertical asymptote of the function is x=1

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