# How do you find the Vertical, Horizontal, and Oblique Asymptote given #(x+3)/ (x^2+4x+3)#?

vertical asymptote x = -1

horizontal asymptote y = 0

The first step is to factorise and simplify f(x).

The denominator of f(x) cannot be zero as this would be undefined. Equating the denominator and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

solve: x + 1 = 0 → x = -1 is the asymptote

Horizontal asymptotes occur as

divide terms on numerator/denominator by x

Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (numerator-degree 0 , denominator-degree 1 ) Hence there are no oblique asymptotes. graph{(1)/(x+1) [-10, 10, -5, 5]}

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To find the vertical asymptotes of a rational function, set the denominator equal to zero and solve for ( x ). These values are the vertical asymptotes. To find the horizontal asymptote, 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 degrees are equal, divide the leading coefficients of both terms to find the horizontal asymptote. If the degree of the numerator is greater, there is no horizontal asymptote. To find the oblique (slant) asymptote, perform polynomial long division or synthetic division to divide the numerator by the denominator. The quotient represents the equation of the 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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