# How do you find the vertical, horizontal or slant asymptotes for #f(x)= (-10x+3)/(8x+2)#?

vertical asymptote

horizontal asymptote

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

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{(-10x+3)/(8x+2) [-10, 10, -5, 5]}

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To find the vertical asymptote(s) of the function ( f(x) = \frac{-10x + 3}{8x + 2} ), set the denominator equal to zero and solve for ( x ). There's one vertical asymptote at ( x = -\frac{1}{4} ).

To find the horizontal asymptote, compare the degrees of the numerator and denominator. Since both have the same degree (1), divide the leading coefficients. Therefore, the horizontal asymptote is ( y = -\frac{10}{8} = -\frac{5}{4} ).

There are no slant asymptotes since the degree of the numerator is not exactly one more than the degree of the denominator.

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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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