Identify the range of the function \( g(x) = -\sqrt{2x + 10} \).

To find the range of the function \( g(x) = -\sqrt{2x + 10} \), we first need to identify the domain. The expression under the square root, \( 2x + 10 \), must be non-negative, so we solve \( 2x + 10 \geq 0 \), leading to \( x \geq -5 \). Now, as \( x \) increases from \(-5\) to \(\infty\), \( 2x + 10 \) takes on values starting from \(0\) to \(\infty\), and consequently, \(-\sqrt{2x + 10}\) will range from \(0\) down towards \(-\infty\). Thus, the range of \( g(x) \) is \( (-\infty, 0] \). This means that \( g(x) \) produces values that are zero or negative, making it a fun function to explore if you enjoy playing around with numbers that "sink" down below zero!