Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
-$f ( x ) = \sin \left( x + \frac { \pi } { 2 } \right) ; g ( x ) = \sin \left( x + \frac { \pi } { 3 } \right)$
A) Translate to the right $\frac { 5 \pi } { 6 }$ units
B) Translate to the left $\frac { \pi } { 6 }$ units
C) Translate to the right $\frac { \pi } { 6 }$ units
D) Translate to the left $\frac { 5 \pi } { 6 }$ units

Question

Quizplus · Accepted Answer

To obtain $f(x)$ from $g(x)$, the graph needs to be translated to the left by $\frac{\pi}{6}$ units, since $f(x) = \sin\left(x + \frac{\pi}{2}\right)$ can be derived from $g(x) = \sin\left(x + \frac{\pi}{3}\right)$ by shifting $g(x)$ to the left to align the phase shifts, i.e., $\frac{\pi}{2} - \frac{\pi}{3} = \frac{\pi}{6}$.

Describe the Transformations Required to Obtain the Graph of the Function