How do you identify all asymptotes for #f(x)=(4x)/(x^21)#?
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is nonzero for these values then they are vertical asymptotes.
Horizontal asymptotes occur as
Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (numeratordegree 1 , denominatordegree 2) Hence there are no oblique asymptotes. graph{(4x)/(x^21) [10, 10, 5, 5]}
By signing up, you agree to our Terms of Service and Privacy Policy
To identify all asymptotes for ( f(x) = \frac{4x}{x^2  1} ), we need to consider both vertical and horizontal asymptotes.

Vertical Asymptotes: Vertical asymptotes occur where the denominator of the function becomes zero, but the numerator does not. For ( f(x) = \frac{4x}{x^2  1} ), the denominator becomes zero when ( x^2  1 = 0 ). Solving this equation gives us ( x = 1 ) and ( x = 1 ). Therefore, the vertical asymptotes are at ( x = 1 ) and ( x = 1 ).

Horizontal Asymptotes: Horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 1, and the degree of the denominator is 2. Therefore, there is a horizontal asymptote. To find it, we divide the leading coefficient of the numerator by the leading coefficient of the denominator. In this case, ( \frac{4}{1} = 4 ). So, the horizontal asymptote is ( y = 4 ).
In summary, the asymptotes for ( f(x) = \frac{4x}{x^2  1} ) are:
 Vertical asymptotes at ( x = 1 ) and ( x = 1 ).
 Horizontal asymptote at ( y = 4 ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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 the vertical, horizontal or slant asymptotes for #(3x)/(x^2+2)#?
 How do you find the inverse of #y=3x+1# and is it a function?
 Let # f(x) = x^2 # and ##, how do you find each of the compositions?
 What is the importance of inverse functions?
 How do you describe the transformation of #f(x)=sqrt(x9)# from a common function that occurs and sketch the graph?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7