Answer is option C.
Step-by-step explanation:
From the graph we see that
When x = -2, y = 8
When x = -1, y = 5
When x = 0, y= 4
When x = 1, y = 5
When x = 2 y=6
When x = 6 y=10
Hence we get the plotted points as (-2,8) , (-1,5) ,(0,4), (1,5) , (2,6), (6,10)
Now consider the function given in option C. Using the above values of x we can get the corresponding values of y.
y = \left \{ {{x^{2} +4, x<2} \atop {x+4, x>=2}} \right.
When x = -2, y = x^{2} +4 = 8
When x = -1, y = x^{2} +4 = 5
When x = 0, y = x^{2} +4 = 4
When x = 1, y = x^{2} +4 = 5
When x = 2, y = x +4 = 6
When x = 6, y = x +4 = 10
These points match the points obtained from the graph as shown above.
Hence option C is the function plotted in the graph
Note : By substituting the above points in the functions given in option A, B and D, we can see that the result does not match the points obtained from the graph.
