Notice that over the interval [-1 , 1.5], the function f seems to be equal to x^2.
Furthermore, over the interval [-3 , -1], the function f seems to be a straight line of slope equal to 2 and y-intercept equal to 3.
Therefore, we can write down:

On the other hand, the function g seems to be a straight line of slope 4 and y-intercept equal to -6 from x=0 to x=2, and something similar to 2x^2 from X=2 to x=4.5, but with its vertex at x=3

Notice that the vertical lengths of g seem to be twice those of f, so out first guess may be to write:

Additionally, the function seems to be displaced 3 units to the right, so:

Observe that since the domain of f is equal to [-3 , 1.5], then x has to be in the interval [0 , 4.5] for f(x-3) to be well defined. Also, a change in the correspondence rule of f happens at x=-1, and for g it happens at x=2.
In terms of f, this should happen at x-3=-1, which is equivalent to x=2.
Finally, observe that:

Therefore:
