# How do you find the vertical, horizontal or slant asymptotes for #y=4/(x+4 ) #?

vertical asymptote x= -4

horizontal asymptote y = 0

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

solve: x + 4 = 0 → x = -4 is the equation.

If the degree of the numerator is less than the degree of the denominator, as in this case , numerator degree 0, denominator degree 1 then the equation is always y = 0.

Here is the graph of the function as an illustration. graph{4/(x+4) [-10, 10, -5, 5]}

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

To find the vertical asymptote of (y = \frac{4}{x+4}), set the denominator equal to zero and solve for (x). In this case, (x + 4 = 0) gives (x = -4). Therefore, there is a vertical asymptote at (x = -4).

To find the horizontal asymptote, observe the behavior of the function as (x) approaches positive or negative infinity. As (x) becomes very large (positive or negative), the term (4/(x+4)) approaches zero since the denominator becomes much larger than the numerator. Therefore, the horizontal asymptote is (y = 0).

Since the degree of the numerator is less than the degree of the denominator, there is no slant (oblique) asymptote for this function.

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.

- How do you find vertical, horizontal and oblique asymptotes for #(x^4 - 2x + 3) / (6 - 5x^3)#?
- How do you find the asymptotes for #f(x)=(-7x + 5) / (x^2 + 8x -20)#?
- How do you find the vertical, horizontal or slant asymptotes for # f(x) = e^(1/x)#?
- How do you find the asymptote of an exponential function?
- How do you find the domain and range and is it a function given points #{(1,-2), (1,4), (1,-6), (1,0)}#?

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