Graph the following function over a two-period interval. Give the period and the amplitude.
\[
y=-3 \cos 5 x
\]
What is the period of the function $y=-3 \cos 5 x$ ?
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)
What is the amplitude of the function $y=-3 \cos 5 x$ ?
(Type an integer or a simplified fraction.)
Which of the following is the correct graph of the function $y=-3 \cos 5 x$ ?
A.
B.
C.
D.

Step 1 ：First, we need to find the period of the function. The period of a function of the form \(y = a \cos (bx)\) or \(y = a \sin (bx)\) is given by \(\frac{2\pi}{|b|}\).

Step 2 ：In this case, \(b = 5\), so the period of the function \(y = -3 \cos 5x\) is \(\frac{2\pi}{5}\).

Step 3 ：Next, we need to find the amplitude of the function. The amplitude of a function of the form \(y = a \cos (bx)\) or \(y = a \sin (bx)\) is given by \(|a|\).

Step 4 ：In this case, \(a = -3\), so the amplitude of the function \(y = -3 \cos 5x\) is \(3\).

Step 5 ：Finally, we need to graph the function over a two-period interval. The function \(y = -3 \cos 5x\) is a cosine function with a period of \(\frac{2\pi}{5}\) and an amplitude of 3, and it is reflected about the x-axis because the coefficient of the cosine function is negative.

Step 6 ：The graph of the function \(y = -3 \cos 5x\) over a two-period interval is shown below:

Step 7 ：\[\text{Graph of } y = -3 \cos 5x\]

Step 8 ：\[\text{The period of the function } y = -3 \cos 5x \text{ is } \boxed{\frac{2\pi}{5}}.\]

Step 9 ：\[\text{The amplitude of the function } y = -3 \cos 5x \text{ is } \boxed{3}.\]