What are the asymptotes for #(x + 4)/(x^2+x-6)#?

Answer 1

In cases like this, you must often rewrite (factorise)

#=(x+4)/((x-2)(x+3))#

Since the numerator may not be #=0# we conclude: #x!=2andx!=-3#

So #x=2andx=-3# are the vertical asymptotes.

As #x# gets larger, the #4,-2and3# makes less and less of a difference, so it begins to look like: #x/(x*x)=1/x# which will get smaller and smaller.

So #y=0# is the horizontal asymptote. graph{(x+4)/(x^2+x-6) [-10, 10, -5, 5]}

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Answer 2

Xavier Alonso

The asymptotes for the function ( \frac{x + 4}{x^2+x-6} ) are ( x = -3 ) and ( x = 2 ).

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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.