*Question: What are the vertical and horizontal asymptote of f(x)=3x-1/12x+4 *

Vertical asymptotes occur when there is a division by zero. (i.e. the denominator = 0)

y = (3x - 1)/(12x + 4)

The denomijnator, (12x + 4) is zero when x = -3.

**Vertical asymptote occurs at x = -3**

Horizontal asymptotes are those values that the function tends to as x tends to plus or minus infinity.

y = (3x - 1)/(12x + 4)

y = (3x + 1 - 2)/{4(3x + 1)}

y = (3x + 1)/{4(3x + 1)} - 2/(4(3x + 1)}

y = 1/4 - 1/(6x + 2)

As x tends to plus or minus infinity, 1/(6x + 2) tends to zero.

So y tends to 1/4.

**The horizontal asymptote is y = 1/4**