1. The problem asks us to write an expression for the function $g(x)$ which is a translation of the function $f(x) = \sqrt{x}$. 2. The translation is 3 units down and 5 units to the left. 3. The general rule for translating a function $f(x)$ is: - Horizontal translation by $h$ units: $f(x+h)$ if moving left, $f(x-h)$ if moving right. - Vertical translation by $k$ units: $f(x) + k$ if moving up, $f(x) - k$ if moving down. 4. Since $g(x)$ is translated 5 units to the left, replace $x$ by $x + 5$. 5. Since $g(x)$ is translated 3 units down, subtract 3 from the function. 6. Therefore, the expression for $g(x)$ is: $$g(x) = \sqrt{x + 5} - 3$$ 7. This expression is already simplified. 8. The graph of $g(x)$ starts at $(-5, -3)$ because when $x = -5$, inside the square root is zero, and the function value is $-3$. Final answer: $$g(x) = \sqrt{x + 5} - 3$$