1 find the vertical and horizontal asymptotes of fx 3x2 1

1) find the vertical and horizontal asymptotes of f(x)= (3x^2 + 1) / (x^2 + x + 9)

2) f(x) = x^2 -36/ x+6

a) what is the y-intercept

b) what are the vertical and horizontal asymptotes if any

4) Square root of x/ x^2-6x-16 find the domain

1) f(x) = (3x^2 +1)/(x^2 +x+9)

To get vertical asymtotes : equate denominator to 0

x^2 +x+9 =0

There are no real solutions to above quadratic.

No vertical asymtote

Horizontal Asymtote:

y = 3x^2/x^2 =3----> y = 3

2) f(x) = (x^2 -36) /(x +6)

a) Y intercept : plug x= 0 ; f(0) = -36/6 = -6

( 0, -6)

b) f(x) = (x^2 -36) /(x +6)

= (x+6)(x-6)/(x+6) = x-6

This has no vertical asymptote

Since the degree of the numerator is one greater than the degree of the denominator, it will have a slant asymptote (not a horizontal one)