Given that g(0) has a period of 2 and f(0) has a period of 4, we can determine the function rule for g(0) by using the property that f(0) has a period half that of g(0).
Since g(0) has a period of 2, the general form of the function rule for g(0) can be written as:
g(x) = A sin(Bx + C)
Where A is the amplitude, B is the frequency (1/period), and C is the phase shift.
We already know that g(0) = 0, which means that C = 0.
Since the period of g(0) is 2, then the frequency B is given by 1/2. Therefore, the function rule for g(0) can be written as:
g(x) = A sin((1/2)x)
Now, we are given that the amplitude of f(x) is twice the amplitude of g(x). Since the amplitude of f(x) is 4, the amplitude of g(x) is 2. Therefore, the function rule for g(x) is:
g(x) = 2 sin((1/2)x)
The functions f(0) and g(0) are sine functions, where
f(0) = g(0) = 0. The
amplitude of f(0) is twice the amplitude of g(0). The period of f(f) is one-half the period of g(0). If g(0) has a period
of 2 and f (5) = 4, write
the function rule for g(0).
Explain your reasoning.
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1 answer