What is the domain of the function \(f(x)=\sqrt{2x+8}\)?

Correct answer: \([-4,\infty)\)

For a real-valued square-root function, the expression inside the radical must be non-negative. Thus, \(2x+8\geq 0\), so \(2x\geq -8\) and \(x\geq -4\). Therefore, the domain is \([-4,\infty)\). Option B incorrectly includes values less than \(-4\); for example, at \(x=-5\), \(2x+8=-2\), which has no real square root. Exam tip: for a real square-root function, set the radicand greater than or equal to zero.