How do you find the asymptotes for # f(x)= (x+5)/(x+3)#?

Answer 1

vertical asymptote at x = -3
horizontal asymptote at y = 1

Vertical asymptotes occur when the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.

solve x + 3 = 0 #rArr x = - 3 #

Horizontal asymptotes occur as #lim_(x→±∞) f(x) → 0#

If the degree of the numerator and denominator are equal , the equation can be found by taking the ratio of leading coefficients. Here they are both degree 1.

#rArr y = 1/1 = 1 " is the equation"#

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

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Answer 2

Liam Brennan

To find the asymptotes of ( f(x) = \frac{x+5}{x+3} ), determine if there are any vertical or horizontal asymptotes by analyzing the behavior of the function as ( x ) approaches infinity or negative infinity and by examining the behavior around any points of discontinuity. In this case, there is a vertical asymptote at ( x = -3 ) because the denominator becomes zero at that point. There are no horizontal asymptotes.

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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.