1 what is the period of this function 2 what is the amplitud

  
1: what is the period of this function?
2: what is the amplitude of this function
3: define function g (a) to represent the behavior of the graphed function

Solution

Solution:

1. As we can see from the given graph

that it g(a) is repeating same pattern during certain interval and that interval would be the period of function

Let\'s us take point a = -2 and at this point it starts rising and we can again see that it again start rising at a = 2

therefore interval = 2- (-2) = 4

2. As we can see graph has middle line x axis and it is going maximum up 2.5 units and maximum down 2.5 units

therefore it has amplitude of 2.5 units

3. Since function is maximum positive at x = 0 and maximum negative at x = 2 and -2

Now know that cosine function is maximum positive at x =0 and has either max 1 or min -1 with 2 period

but if we compare this with cosine function then we found that this graph pattern is same as cosing but have different amplitude and periods

Now

If let g(a) = A cos(n/4) is our resultant graph

then from above A= 2.5 and

g(a) = 2.5 Cos(n/4)

Answer