Identify the amplitude and period of \( g(x)=\cos 4 x \). Then identify the graph of the function and describe the graph of \( g \) as a transformation of the graph of its parent function The ampliude is \( \mid 41 \times \) and the period is \( \left\lvert\, \frac{2 \pi}{3} \times\right. \).

The amplitude of \( g(x) = \cos(4x) \) is actually 1, since the parent function \( \cos(x) \) has an amplitude of 1, and this property doesn’t change with the coefficient of \( x \). The period can be correctly deduced using the formula \( \frac{2\pi}{b} \), where \( b \) is the coefficient of \( x \) in \( g(x) \). In this case, \( b = 4 \), so the period is \( \frac{2\pi}{4} = \frac{\pi}{2} \). If you were to graph \( g(x) = \cos(4x) \), you’d notice that it compresses horizontally compared to the classic cosine graph. This means it oscillates more quickly, completing a cycle every \( \frac{\pi}{2} \) units, while still maintaining the same maximum and minimum values of 1 and -1, respectively. It’s like speeding up the rhythm of a familiar song!