Question

question 4 of 10
describe the transformation of ( f(x)=sin x ) to ( g(x)=sin left(x+\frac{pi}{3}
ight) ).
a. ( f(x) ) is shifted ( \frac{pi}{3} ) units up.
b. ( f(x) ) is shifted ( \frac{pi}{3} ) units down.
c. ( f(x) ) is shifted ( \frac{pi}{3} ) units to the left.
d. ( f(x) ) is shifted ( \frac{pi}{3} ) units to the right.

Explanation:

For a function transformation of the form \( y = f(x + h) \), where \( h > 0 \), the graph of \( f(x) \) is shifted \( h \) units to the left. Here, \( f(x) = \sin x \) and \( g(x) = \sin(x + \frac{\pi}{3}) \), so \( h = \frac{\pi}{3} \), meaning \( f(x) \) is shifted \( \frac{\pi}{3} \) units left.

Answer:

C. \( f(x) \) is shifted \( \frac{\pi}{3} \) units to the left.