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How can you tell when a function has no vertical asymptotes?

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for example (2x+1)/(x^2+x+1) has no vertical asymptotes but why?

asked Nov 20, 2014 in PRECALCULUS by anonymous

1 Answer

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The rational function is f(x) = (2x + 1)/(x2 + x + 1)

Vertical asymptote can be found by making denominator = 0.

x2 + x + 1 = 0

Compare it to quadratic equation ax2 + bx + c = 0.

a = 1, b = 1, c = 1

Discriminant b2 - 4ac = (1)2 - 4(1)(1)

= 1 - 4 = - 3

b2 - 4ac < 0

The discriminant is negative then the equation x2 + x + 1 = 0 has two imaginary solutions.

Real solutions are zeros of the function.

Since the denominator has no zeros then there are no vertical asymptotes.

answered Nov 20, 2014 by david Expert

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