# How do you find the horizontal asymptote for #(4x)/(x-3) #?

I found

To find this line there is a trick!

You can "see" this graphically: graph{(4x)/(x-3) [-25.66, 25.65, -12.83, 12.83]}

Hope it helps!

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To find the horizontal asymptote of the function ( \frac{4x}{x-3} ), you can use the concept of limits as ( x ) approaches positive or negative infinity.

As ( x ) approaches infinity, the terms in the numerator and denominator with the highest power dominate the fraction. In this case, the highest power terms are ( 4x ) and ( x ) respectively. So, the horizontal asymptote can be found by dividing the leading coefficient of the numerator by the leading coefficient of the denominator.

Therefore, the horizontal asymptote is ( y = \frac{4}{1} = 4 ).

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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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