We can identify the range by looking at all possible y values or the result after you input an x in the g(x) function. We see that in the g(x) function, the vertex of the quadratic graph lies on (0,2) when we graph it. Thus, any possible y value must be less than or equal to (0,2) because the slope is pointing down due to the negative coefficient attached to the x, making it have a maximum.
Thus all y values or the range of g(x) must be {y<=2}
