Question

question 9 of 30
describe the transformation of ( f(x)=cos x ) to ( g(x)=cos left(x-\frac{pi}{3}
ight) ).

a. ( f(x) ) is shifted ( \frac{pi}{3} ) units down.
b. ( f(x) ) is shifted ( \frac{pi}{3} ) units to the left.
c. ( f(x) ) is shifted ( \frac{pi}{3} ) units to the right.
d. ( f(x) ) is shifted ( \frac{pi}{3} ) units up.

Explanation:

For a function \( f(x) = \cos x \), the transformation \( g(x) = \cos(x - h) \) (where \( h > 0 \)) results in a horizontal shift of \( f(x) \) to the right by \( h \) units. Here, \( h = \frac{\pi}{4} \), so \( f(x) \) is shifted \( \frac{\pi}{4} \) units to the right.

Answer:

C. \( f(x) \) is shifted \( \frac{\pi}{4} \) units to the right.