What is the range of the function \(f(x)=(x+5)^2\)?

Correct answer: \([0,\infty)\)

For every real \(x\), \((x+5)^2\geq 0\). The minimum value is \(0\), attained when \(x=-5\), and arbitrarily large values are possible. Hence the range is \([0,\infty)\). \([5,\infty)\) is incorrect because the \(+5\) is inside the square; it shifts the vertex horizontally and does not make the minimum function value 5. Exam tip: For a squared expression, find the input that makes the squared part zero to identify the minimum value.