Question

If f(x) = 2 sin(x) and g(x) = sin(2x), which of the following statements is true?

A
The graph of g(x) and the graph of f(x) are identical
The amplitude of g(x) is greater than the amplitude of f(x)
The amplitude of f(x) is greater than the amplitude of g(2)
D
O
The period of f(x) is half of the period of g(x)

Answer 1

The correct options are;

The amplitude of f(x) is greater than the amplitude of g(x)

Step-by-step explanation;

The given functions are plotted

From the graphs, we have;

The amplitude of f(x) is larger than the amplitude of g(x)

The graphs of g(x) and f(x) are not identical

The period (the time taken to complete one cycle) of g(x) is half the period of f(x)

The observed properties are due to the fact that the maximum value of the sine function are ±1, and the period of the sine function is 2·π or 360°.