How to find the asymptotes of #f(x) =(9x^2 – 36)/( x^2  9)# ?
Vertical asymptotes occur when the denominator equals
Vertical Asymptotes :
Horizontal Asymptotes :
Find the highest exponents in the numerator and denominator, then divide ...
So,
Here is a graph. The dotted lines are the asymptotes ...
Hope that helped
By signing up, you agree to our Terms of Service and Privacy Policy
To find the asymptotes of ( f(x) = \frac{9x^2  36}{x^2  9} ):

Check for vertical asymptotes by finding the values of ( x ) that make the denominator zero. In this case, set ( x^2  9 = 0 ) and solve for ( x ). ( x^2  9 = 0 ) ( (x  3)(x + 3) = 0 ) ( x = 3 ) or ( x = 3 )

These values ( x = 3 ) and ( x = 3 ) represent vertical asymptotes.

Check for horizontal asymptotes by comparing the degrees of the numerator and the denominator. Since both have the same degree (2), divide the leading coefficients of the numerator and denominator. ( \lim_{x \to \pm \infty} \frac{9x^2}{x^2} = 9 )

The horizontal asymptote is ( y = 9 ).
Therefore, the asymptotes of the function ( f(x) = \frac{9x^2  36}{x^2  9} ) are:
 Vertical asymptotes at ( x = 3 ) and ( x = 3 ).
 Horizontal asymptote at ( y = 9 ).
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.
 If #f(x)=x^2+4x# and #g(x)=3x5#, how do you find #(f(g(x))# and #g(f(x))#?
 How do you find the asymptotes for #y= (14x)/(x^4 +1)^(1/4)#?
 How do you graph the piecewise function #3x+2 , if x ≠ 1#, #8 , if x = 1#?
 How do you determine whether the graph of #y=sqrt(2x^2)# is symmetric with respect to the x, y axis?
 How do you find the inverse of #f(x) = x^3 + 4#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7