# How do you find the slant asymptote of #f(x) =( x^2 + 3x - 3) / (x+4)#?

The slant asymptote is

Let's do the long division

Therefore,

So,

graph{(y-(x^2+3x-3)/(x+4))(y-x+1)=0 [-10, 10, -5, 5]}

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Slant asymptote:

By division,

Rearranged,

asymptotes

Separately,

y-x+1=0 gives a slant asymptote and

x+4=0 gives a vertical asymptote.

graph{((y-x+1)(x+4)-1)(y-x+1)(x+0.000001y+4)=0 [-23, 23.02, -12.7, 12.6]}

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To find the slant asymptote of ( f(x) = \frac{x^2 + 3x - 3}{x+4} ), perform polynomial long division. Divide the numerator ( x^2 + 3x - 3 ) by the denominator ( x + 4 ). The quotient will be the equation of the slant asymptote.

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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.

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.

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.

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