Answer:
A. y < x² + 6 ; y > x² - 4
Step-by-step explanation:
The area between the two functions represent the system of inequalities graphed.
Given the parent function f(x) = x², if we translated 6 units up we get g(x) = x² + 6, which corresponds to the upper function in the graph. Then, one restriction is y < x² + 6 (notice that the dotted line indicates the equal sign is not included).
If we translate f(x) 4 units down, we get h(x) = x² - 4, which corresponds to the lower function in the graph. Then, the other restriction is y > x² - 4 (again, the equal sign is not included).
Taking for example the point (0, 0), which correspond to the solution of the system, we get
0 < 0² + 6
0 < 6
0 > 0² - 4
0 > -4
which is correct
