# How do you find the asymptotes for #f(x)= (x-4)/(x^2-4)#?

vertical asymptotes at x = ± 2

horizontal asymptote at y = 0

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

If the degree of the numerator is less than the degree of the denominator, as in this case (degree 1 < degree 2 ) then the equation is y = 0.

Here is the graph of the function as an illustration. graph{(x-4)/(x^2-4) [-10, 10, -5, 5]}

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

To find the asymptotes for the function ( f(x) = \frac{x - 4}{x^2 - 4} ), you first identify any vertical asymptotes by determining where the denominator equals zero. In this case, the denominator ( x^2 - 4 ) equals zero when ( x = 2 ) or ( x = -2 ). Therefore, the vertical asymptotes are ( x = 2 ) and ( x = -2 ).

Next, you check for horizontal asymptotes. To do this, you compare the degrees of the numerator and denominator of the function. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ). If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is greater, there is no horizontal asymptote.

In this case, the degree of the numerator is 1 and the degree of the denominator is 2. Therefore, there is a horizontal asymptote at ( y = 0 ).

So, the asymptotes for the function ( f(x) = \frac{x - 4}{x^2 - 4} ) are ( x = 2 ), ( x = -2 ), and ( y = 0 ).

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 range of a function like #f(x)=5x^2#?
- How do you find the Vertical, Horizontal, and Oblique Asymptote given #x /( 4x^2+7x-2)#?
- Suppose #I# is an interval and function #f:I->R# and #x in I# . Is it true that #f(x)=1/x# is not bounded function for #I=(0,1)# ?. How do we prove that ?
- If #f(x)=-2x^2-5x# and #g(x)=3x+2#, how do you find the domain and range of f(x), g(x), and f(g(x))?
- How do you find the end behavior of #f(x) = -x^(4) + 6x^(3) - 9^(2)#?

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