# How do you find the vertical, horizontal or slant asymptotes for #y=(3x+1)/(2-x)#?

vertical asymptote at x = 2

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 non-zero 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 degree 1) Hence there are no slant asymptotes. graph{(3x+1)/(2-x) [-20, 20, -10, 10]}

By signing up, you agree to our Terms of Service and Privacy Policy

To find the vertical asymptotes of ( y = \frac{3x+1}{2-x} ), determine the values of ( x ) that make the denominator zero. In this case, the denominator becomes zero when ( x = 2 ). Thus, there is a vertical asymptote at ( x = 2 ).

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 ). In this case, since the degree of the numerator (which is 1) is less than the degree of the denominator (which is 1), the horizontal asymptote is at ( y = 0 ).

To determine if there is a slant asymptote, perform polynomial long division or synthetic division to divide the numerator by the denominator. If the resulting quotient is a polynomial, there is no slant asymptote. If the quotient is not a polynomial, but a linear expression, that linear expression represents the slant asymptote.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7