Graph the following function over a two-period interval. Give the period and the amplitude.
$y = \frac{1}{5} \cos \frac{π}{2} x$
What is the period of the function $y = \frac{1}{5} \cos \frac{π}{2} x$ ?
(Simplify your answer. Type an exact answer, using $π$ as needed. Use integers or fractions for any numbers in the expression.)
What is the amplitude of the function $y = \frac{1}{5} \cos \frac{π}{2} x$ ?
(Type an integer or a simplified fraction.)
Graph the function $y = \frac{1}{5} \cos \frac{π}{2} x$ . Choose the correct graph below.
A.
B.
c.
D.

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Answer

To graph the function $y = \frac{1}{5} \cos \frac{π}{2} x$ , we note that the function has a period of $4$ and an amplitude of $\frac{1}{5}$ . The function starts at its maximum value of $\frac{1}{5}$ at $x = 0$ , decreases to $0$ at $x = 1$ , reaches its minimum value of $- \frac{1}{5}$ at $x = 2$ , returns to $0$ at $x = 3$ , and finally returns to its maximum value at $x = 4$ . This pattern repeats every $4$ units.

Steps

Step 1 ：The graph of $y = \frac{1}{5} \cos \frac{π}{2} x$ passes through one full period as $\frac{π}{2} x$ ranges from $0$ to $2 π,$ which means $x$ ranges from $0$ to $4 .$

Step 2 ：The amplitude of the function $y = \frac{1}{5} \cos \frac{π}{2} x$ is the absolute value of the coefficient of the cosine function, which is $\frac{1}{5}$ .

Step 3 ：To graph the function $y = \frac{1}{5} \cos \frac{π}{2} x$ , we note that the function has a period of $4$ and an amplitude of $\frac{1}{5}$ . The function starts at its maximum value of $\frac{1}{5}$ at $x = 0$ , decreases to $0$ at $x = 1$ , reaches its minimum value of $- \frac{1}{5}$ at $x = 2$ , returns to $0$ at $x = 3$ , and finally returns to its maximum value at $x = 4$ . This pattern repeats every $4$ units.

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