Find the vertical and horizontal any mottoes of the function

Find the vertical and horizontal any mottoes of the function. (Enter answer as a comma -suppressed list f(x) = 4x^-1 + 1/x^2 + x + 16 Find the vertical and horizontal any mottoes of the function. (Enter answer as a comma-suppressed list f(x) = 4 + x/4 - x

Solution

f(x) = (4x^1 +1)/( x^2 +x+16)

Vertical asymtote : x^2 +x +16 =0

No real solution exists , so vertical asymtote

Horizontal asymtote :

y = 4x^2/x^2 = 4

y = 4

f(x) = (4+x)/( 4 -x)

vertical asymtote :

4-x =0 ; x=4

horizntal asymtote : y = x/-x = -1

y = -1