The domain of \( h(x)=\sqrt{-x}+6 \) is \( (-\infty, 0] \) (Type your answer in interval notation.) The range of \( h(x)=\sqrt{-x}+6 \) is \( \square \). (Type your answer in interval notation.)

The function \( h(x) = \sqrt{-x} + 6 \) has a domain of \( (-\infty, 0] \) because the expression inside the square root must be non-negative, which is true for any \( x \) less than or equal to 0. To find the range, notice that as \( x \) approaches \( -\infty \), \( \sqrt{-x} \) becomes very large, leading \( h(x) \) to tend towards \( \infty \). When \( x = 0 \), \( h(x) = \sqrt{0} + 6 = 6 \). Thus, the range of \( h(x) \) is \( [6, \infty) \).