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What are the asymptotes for #F(X) = (1/ X^2) - 2#?

Answer 1

Christian Antunez

Vertical asymptote at #x=0#
Horizontal asymptote at #y=-2#

Vertical asymptotes occur at points where the denominator is zero, so in this case at #x=0#.

Horizontal asymptotes occur at #lim_(x->+-oo)F(x)=-2#

graph{1/(x^2)-2 [-4.933, 4.932, -2.464, 2.47]}

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Answer 2

Madelyn Anderson

To find the asymptotes of the function ( f(x) = \frac{1}{x^2} - 2 ), we need to identify where the function approaches infinity or negative infinity.

Vertical asymptotes occur where the function approaches infinity or negative infinity as ( x ) approaches certain values. Since ( x^2 ) cannot be zero, there are no vertical asymptotes for this function.
Horizontal asymptotes occur as ( x ) approaches positive or negative infinity. For the given function, as ( x ) approaches positive or negative infinity, the term ( \frac{1}{x^2} ) approaches zero. Therefore, the horizontal asymptote is at ( y = -2 ).

So, the horizontal asymptote for ( f(x) = \frac{1}{x^2} - 2 ) is ( y = -2 ). There are no vertical asymptotes.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.