Question: Select the correct answer from each drop-down menu. Which transformation causes the described change in the graph of the function $f(x)=\sin(x)$? The transformation Choose an answer results in a vertical shift down. The transformation Choose an answer results in a horizontal shift left. The transformation Choose an answer results in a vertical shift up. The transformation Choose an answer results in a horizontal shift right.

1. **State the problem:** We need to identify which transformations cause vertical and horizontal shifts in the graph of the function $f(x)=\sin(x)$. 2. **Recall the transformations:** - A vertical shift up or down is caused by adding or subtracting a constant outside the function: $f(x) + k$ shifts the graph vertically by $k$ units. - A horizontal shift left or right is caused by adding or subtracting a constant inside the function argument: $f(x - h)$ shifts the graph horizontally by $h$ units. 3. **Vertical shifts:** - $f(x) + k$ shifts the graph vertically. - If $k > 0$, the graph shifts up. - If $k < 0$, the graph shifts down. 4. **Horizontal shifts:** - $f(x - h)$ shifts the graph horizontally. - If $h > 0$, the graph shifts right. - If $h < 0$, the graph shifts left. 5. **Answering each part:** - Vertical shift down: transformation is $f(x) - k$ where $k > 0$. - Horizontal shift left: transformation is $f(x + h)$ where $h > 0$. - Vertical shift up: transformation is $f(x) + k$ where $k > 0$. - Horizontal shift right: transformation is $f(x - h)$ where $h > 0$. **Final answers:** - Vertical shift down: $f(x) - k$ - Horizontal shift left: $f(x + h)$ - Vertical shift up: $f(x) + k$ - Horizontal shift right: $f(x - h)$