I'm having some troubles. I can't think of an example to this question.

Question

Give an exmaple of a quadratic whose reciprocal has no vertical asymptotes

I think it's 1/x^2. The question says vertical asymptotes so I'm assuming they mean there will only be one. But I don't think I'm right.

Answer 1

Consider the quadratic function
f(x) = x^2 + 5

the reciprocal function would be g(x) = 1/(x^2 + 5)

there is no real number which would make the denominator zero, the condition for vertical asymptotes.

So there is your example, there would be countless of others

Answer 2

Thank you.

Answer 3

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