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

I found

The horizontal asymptote is a line towards which the curve, described by your function, tends to get as near as possible.

You can plot your function and see this tendency! graph{(3x)/(x+4) [-41.1, 41.07, -20.56, 20.53]}

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To find the horizontal asymptote for the function ( f(x) = \frac{3x}{x+4} ), you need to examine the behavior of the function as ( x ) approaches positive or negative infinity.

For rational functions like this one, if the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ).

In this case, the degree of the numerator is 1 and the degree of the denominator is also 1. To find the horizontal asymptote, divide the leading coefficient of the numerator by the leading coefficient of the denominator:

[ \lim_{x \to \pm \infty} \frac{3x}{x+4} = \frac{3}{1} = 3 ]

So, the horizontal asymptote of ( f(x) ) is ( y = 3 ).

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