Given,
The graph of the curve is shown in the question.
From the graph, it is seen that,
At point x = -1.5, a straight line is passing through the x-axis.
Hence, one zero of the curve is -1.5.
Now, At point 0, the curve is in a cubic form. So the zero of the curve is x = 0 with muliplicity of 3.
Now, At point 2, the curve is in a quadratic form. So the zero of the curve is x = 2 with muliplicity of 2.
Thus, the zeroes of curve is - 1.5, 0, 0, 0, 2 and 2.
The possible function of the curve is,
[tex](x)^3\mleft(x-2\mright)^2(x+\frac{3}{2})[/tex]
Hence, the function of the curve is (x)^3(x-2)^2(x+3/2).
