g(x)=5-7/2×-3×^2

Right and left behavior refer to what graph approaches as x goes to infinity (right) and negative infinity (left)

if the function is 5 minus 7/(2x-3x^2), then when x gets big positive or big negative 7/(2x-3x^2) goes to 0

and we are just left with 5. So the graph approaches y = 5 (as an asymptote) on both the left and right