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right left behavior of graph

g(x)=5-7/2×-3×^2

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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