Answer:
Option A is the answer.
Explanation:
Equations of the piecewise function is given as
y = x³ - 3
y = x² + 6
We have to find the domain of the sub-functions.
Since a dark point (2, 5) is lying on the graph that means equation is satisfied when we plug in the values of x and y.
y = x³ - 3
5 = 2³ - 3
5 = 8 - 3
5 = 5
y = x² + 6
5 = 2² + 6
5 = 4 + 6
5 = 10
which is not possible.
Therefore, this function represents the lower part of the graph.
y = x³ - 2 x ≤ 2
Now we put hollow point (2, 10) in both the equations,
10 = 2³ - 3
10 = 8 - 3
10 = 5
Again not possible.
y = x² + 6
10 = 2² + 6
10 = 4 + 6
10 = 10
Therefore, Upper portion of the graph is represented by the equation
y = x² + 6 x > 2
Option A is the answer.