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Let
f be a sinusoidal function. The graph of
y=f(x) is given in the
xy-plane. What is the period of
f ?
(A) 2
(B) 3
C 4
(D) 6

Let $f$ be a sinusoidal function. The graph of $y=f(x)$ is given in the $x y$ -plane. What is the period of $f$ ? $\newline$ (A) $2$ $\newline$ (B) $3$ $\newline$ C $4$ $\newline$ (D) $6$

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Write equations of cosine functions using properties

Full solution

Q. Let

f

be a sinusoidal function. The graph of

y=f(x)

is given in the

x y

-plane. What is the period of

f

?

\newline

(A)

2

\newline

(B)

3

\newline

C

4

\newline

(D)

6

Identify Period Definition: To determine the period of the sinusoidal function $f$ , we need to identify how long it takes for the function to complete one full cycle on the graph. The period is the distance along the $x$ -axis between two consecutive points where the function starts repeating its values.
Assumption of Graph Analysis: Since we do not have the actual graph provided, we will assume that the graph of the function $f$ has been analyzed, and the distance between two consecutive peaks, troughs, or identical points on the midline has been measured. This distance is the period of the function.
Select Corresponding Value: Based on the given options (A) $2$ , (B) $3$ , (C) $4$ , (D) $6$ , we would select the value that corresponds to the measured distance for one complete cycle of the function $f$ on the graph.
Inability to Determine: Without the graph, we cannot definitively determine the period from the options provided. Therefore, we cannot proceed further in solving this problem without additional information or the graph itself.

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