Answer: The answer is (b) (2, ∞)
Step-by-step explanation: We are given a function f(x) in the figure and we are to select out of the given options that accurately shows the range of the function defined.
[tex]\textup{For }x < 0, \textup{we have}~f(x)=3.[/tex]
[tex]\textup{For }0\leq x<2,\textup{ we have }f(x)=x^2+2\geq 2.[/tex]
[tex]\textup{For }x\geq 2,\textup{ we have }f(x)=\dfrac{1}{2}x+5\geq 5.[/tex]
Therefore, the range of the function f(x) will be greater then or equal to 2. So, the range will be [2, ∞).
Thus, the correct option is (b) (2, ∞).
