1. The problem asks for the function $g(x)$ which is the image of $f(x)$ after a translation 4 units to the left. 2. Translation rules for functions: - Horizontal translation: $f(x - h)$ shifts the graph $h$ units to the right. - Horizontal translation: $f(x + h)$ shifts the graph $h$ units to the left. - Vertical translation: $f(x) + k$ shifts the graph $k$ units upwards. - Vertical translation: $f(x) - k$ shifts the graph $k$ units downwards. 3. Since the translation is 4 units to the left, we use the horizontal translation rule with $h = -4$. 4. Therefore, the translated function is: $$g(x) = f(x + 4)$$ 5. This matches option (b). 6. Summary: To move a function 4 units left, replace $x$ by $x + 4$ in the function. Final answer: $g(x) = f(x + 4)$ (option b).