# How do you find the Vertical, Horizontal, and Oblique Asymptote given #g(x)= (-2x+3) /( 3x+1)#?

horizontal

vertical

testing for horizontal or oblique

for vertical , we look at denominator = 0

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

To find the vertical asymptote, set the denominator equal to zero and solve for x. For the function g(x) = (-2x + 3) / (3x + 1), the vertical asymptote occurs at x = -1/3.

To find the horizontal asymptote, compare the degrees of the numerator and denominator. Since the degree of the numerator (-2x + 3) is less than the degree of the denominator (3x + 1), the horizontal asymptote is y = 0.

To find the oblique asymptote, perform long division or polynomial division between the numerator and denominator. After division, the quotient will represent the oblique asymptote. In this case, performing long division yields y = -2/3x + 3.

So, the vertical asymptote is x = -1/3, the horizontal asymptote is y = 0, and the oblique asymptote is y = -2/3x + 3.

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.

- What is the end behavior and turning points of #y = -2x^3 + 3x - 1#?
- How do you find the vertical, horizontal and slant asymptotes of: #(3x)/(x^2+2)#?
- How do you find the Vertical, Horizontal, and Oblique Asymptote given #y = (x^2 - 5x + 6)/( x - 3)#?
- How do you find the inverse of #y=2(3)^x +1#?
- How do you find the vertical, horizontal or slant asymptotes for #f(x)= (3e^(x))/(2-2e^(x))#?

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