Answer
G
Work Step by Step
According to the text, the graph of the function $y=f(x-d)$ is translated horizontally compared to the graph of $y=f(x)$. If $d$ is greater than zero, the translation is $d$ units to the right and if $d$ is less than zero, the translation is $|d|$ units to the left.
We now compare the equation $y=\sin(x+\frac{\pi}{4})$ to $y=f(x-d)$. Upon inspection, we find that $d=-\frac{\pi}{4}$. Since $d$ is negative, the graph of $y=\sin(x+\frac{\pi}{4})$ will be the same as the graph of $y=\sin x$ except that it will be translated $\frac{\pi}{4}$ units to the left.
Therefore, we need to find a graph which is the same as the graph of $y=\sin x$ except that it is translated $\frac{\pi}{4}$ units to the left. Such a graph is found in option G.
