Answer:
The correct answer is option C.
Step-by-step explanation:
In order to determine the equation of the function, whose graph is given to us in the question, we can use the various coordinates points and the points of discontinuities. Also, we can see the type of graph, for example, a parabolic, straight line etc.
Now, in the graph given in the question, we can see that from x<1, the graph is parabolic given by [tex]y=x^2+2[/tex] and also we can see that x=1 is the discontinuous point, so we will not take x=1 in the domain of the function.
Now when [tex]x\geq 1[/tex], we have the straight line that is given by [tex]y=-x+2[/tex]
where the curve is defined for x=1 also.
So, we will have the step-wise function whose equation will be given by option C.
