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 peak
- The value of the function at x = 0 is -(1/2), where sin(0) = 0, therefore, the function is a cosine function
- The period of the graph is 2·π, which is the period of the parent cosine function
- Therefore, the correct option is [tex]f(x) = -\dfrac{1}{2} \cdot cos(x)[/tex]
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;
[tex]Frequency = \dfrac{2 \cdot \pi }{Period}[/tex]
The period of the graph = π
Therefore;
[tex]The \ frequency = \dfrac{2 \cdot \pi }{\pi} = 2[/tex]
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
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