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

Answer 1

James Allen

#y=0#

#"horizontal asymptotes occur as"#

#lim_(xto+-oo)g(x)toc" (a constant)"#

#"divide terms on numerator/denominator by the highest"# #"power of x, that is "x^2#

#g(x)=(x/x^2+3/x^2)/(x^2/x^2+(4x)/x^2)=(1/x+3/x^2)/(1+4/x)#

#"as "xto+-oo,g(x)to(0+0)/(1+0)#

#rArry=0" is the asymptote"# graph{(x+3)/(x^2+4x) [-10, 10, -5, 5]}

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Answer 2

Chloe Alexander

To find the horizontal asymptote of the function g(x) = (x + 3) / (x(x + 4)), you need to examine the behavior of the function as x approaches positive or negative infinity. By analyzing the degrees of the numerator and denominator, you can determine the horizontal asymptote.

Since the degree of the numerator (1) is less than the degree of the denominator (2), the horizontal asymptote will be at y = 0.

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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.