# How do you find the asymptotes for #y = 4/(x - 3)#?

vertical asymptote at x = 3

horizontal asymptote at y = 0

vertical asymptotes occur as the denominator of a rational function >tends to zero. To find the equation let the denominator = 0

solve : x - 3 = 0 → x = 3 is the equation

If the degree of the numerator is less than the degree of the denominator , as is the case here , then the equation is y = 0

here is the graph of the function as an illustration graph{4/(x-3) [-10, 10, -5, 5]}

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To find the asymptotes of the function ( y = \frac{4}{x - 3} ), you need to determine the values of ( x ) for which the function becomes undefined, as these will be the vertical asymptotes. The vertical asymptote occurs where the denominator becomes zero, which in this case is when ( x - 3 = 0 ). Solve for ( x ) to find the vertical asymptote.

( x - 3 = 0 )

( x = 3 )

Therefore, the vertical asymptote is ( x = 3 ).

There are no horizontal asymptotes for this function.

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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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