What is the vertical and horizontal aysmptote of g(x)=10/x

The vertical asymptote is where the function does not exist (denominator ≠ 0) So set the denominator equal to 0 and solve for x.
vertical asmyptote is x = 0

the horizontal asymptote is the behavoir of the function as x goes to +/- infinity. As x get's larger in value the y-value get's closer and closer to zero.
example: {x = 9, 99, 999, 9999} then {y =1/9, 1/99, 1/999, 1/9999...}
horizontal asmptote is y = 0