Ft is a periodic function with a period of 7 and an amplitude of 3. What is the period and amplitude of the function g(t)=-2f(1/3t)-5?

Can someone show me what I need to do?

To find the period and amplitude of the function g(t) = -2f(1/3t) - 5, we need to understand how the operations affect the period and amplitude of a function.

Let's start with the given function f(t). It is a periodic function with a period of 7 and an amplitude of 3.

1. Period:
The period of a function is the distance between consecutive occurrences of the same point on the graph. Since f(t) has a period of 7, it means that f(t) repeats itself every 7 units along the t-axis.

When we have a function of the form g(at), where 'a' is some constant, it affects the period of the function. For g(t) = f(at), the new period becomes the original period divided by 'a'. In this case, g(t) = -2f(1/3t) means that the original period of f(t) will be multiplied by 3.

So, the period of g(t) will be 7 * 3 = 21.

2. Amplitude:
The amplitude of a function represents the maximum distance the graph reaches from its average or midline. For f(t), the amplitude is 3.

When we multiply a function by a constant, like -2 in g(t) = -2f(1/3t), it affects the amplitude of the function. Multiplying a function by a positive constant scales its amplitude, whereas multiplying by a negative constant also changes the direction (flips) of the graph.

Thus, the amplitude of g(t) will be |-2| * 3 = 6, considering the absolute value of -2.

Therefore, the period of g(t) is 21, and the amplitude of g(t) is 6.

Hope that helps!