1. which function is shown on the graph?
f(x)=1/2cosx
f(x)=−1/2sinx
f(x)=−1/2cosx
f(x)=1/2sinx

2. (picture)

3.(picture)

4.(which equation represents the function on the graph?

5. what is the period of the funtion f(x)=cos2x?

The reasons and responses to the graphs in the question are as follows:

Graph 1.

The amplitude of the first graph is (1/2) which is the height from the midline to the peakThe value of the function at x = 0 is -(1/2), where sin(0) = 0, therefore, the function is a cosine functionThe period of the graph is 2·π, which is the period of the parent cosine functionTherefore, the correct option is

Graph 2: Please find attached the graph of the function g(x) = 2×cos(x)

Graph 3: The frequency of a sinusoidal function is given as follows;

The period of the graph = π

Therefore;

The frequency of the sinusoidal graph is 2

Graph 4.  Required:

To find the equation that represents the function of the graph

Solution;

The period of the function, T = π

The graph of the function has a maximum at x = 0, therefore, the graph is similar to a cosine function, y = cos(B·x)

Where;

B = 2·π/T

Therefore;

B = 2·π/π = 2

Therefore;

The equation that represent the function in the graph is f(x) = cos(2·x)

Question 5. The given function is f(x) = cos(2·x)

The frequency factor in the given function, B = 2

The period, T = 2·π/B

Therefore, T = 2·π/2 = π

The period of the function, f(x) = cos(2·x), is 2

Learn more about sinusoidal function here:

link

link

link

Problem 1

choice C) f(x) = (-1/2)cos(x)

We can rule out anything with sine in it since the graph does not go through the origin. We can rule out choice A as well since plugging x = 0 into f(x) leads to a positive result, when instead we want a negative value. So the only thing left is choice C

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Problem 2

See the attached image

Point A is approximately (1.57, 0) which is exactly (pi/2, 0)
Point B is approximately (3.14, -2) which is exactly (pi, -2)

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Problem 3

1/pi

Period = pi since the graph repeats itself every pi units
Frequency = 1/Period 
Frequency = 1/pi 

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Problem 4

Choice A) f(x) = cos(2x)

This is a cosine function as it doesn't go through the origin. The period is T = pi, so b = 2pi/T = 2pi/pi = 2 is the coefficient of the inner x term. Therefore the function is f(x) = cos(2x)

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