How do you find the vertical, horizontal and slant asymptotes of: #y= (3x+5)/(x6)#?
vertical asymptote at x =6
horizontal asymptote at y = 3
The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is nonzero for this value then it is a vertical asymptote.
Horizontal asymptotes occur as
divide terms on numerator/denominator by x
Slant asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here ( both of degree 1 ) Hence there are no slant asymptotes. graph{(3x+5)/(x6) [20, 20, 10, 10]}
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To find the vertical, horizontal, and slant asymptotes of the function ( y = \frac{3x + 5}{x  6} ), follow these steps:

Vertical asymptotes: Vertical asymptotes occur where the denominator of the rational function equals zero. Set ( x  6 = 0 ) and solve for ( x ) to find the vertical asymptote(s).

Horizontal asymptote: Horizontal asymptotes can be determined by comparing the degrees of the numerator and the denominator of the rational function. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is ( y = 0 ). If the degrees are equal, divide the leading coefficients of the numerator and the denominator to find the horizontal asymptote.

Slant asymptote (if applicable): Slant asymptotes occur when the degree of the numerator is exactly one more than the degree of the denominator. To find the slant asymptote, perform long division of the numerator by the denominator. The quotient obtained represents the equation of the slant asymptote.
Follow these steps to find the vertical, horizontal, and slant asymptotes of the given function.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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