# How do you find vertical, horizontal and oblique asymptotes for #(x+3 )/ (x^2 + 8x + 15)#?

Vertical Asymptotes:

Horizontal Asymptote:

No Oblique Asymptote

To obtain the Horizontal Asymptote, take the limit of the function

To obtain the Vertical Asymptote, equate the factors of the denominator to zero the solve for x.

graph{y=(x+3)/(x^2+8x+15)[-20,20,-10,10]}

God bless....I hope the explanation is useful.

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To find the vertical asymptotes of the function ( \frac{x + 3}{x^2 + 8x + 15} ), determine where the denominator becomes zero. These points will be the vertical asymptotes if the numerator does not also become zero at those points.

To find horizontal and oblique asymptotes, examine the behavior of the function as ( x ) approaches positive or negative infinity. For horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ). If the degree of the numerator is equal to the degree of the denominator, divide the leading coefficients to find the horizontal asymptote. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

For oblique asymptotes, perform polynomial division of the numerator by the denominator. The quotient obtained represents the oblique asymptote. If the degree of the numerator is less than that of the denominator, the oblique asymptote is the x-axis. If the degrees are equal, perform the division and the quotient will be the oblique asymptote. If the degree of the numerator is greater, there is no oblique asymptote.

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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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