Write a function using function notation to describe the situation. find a reasonable domain and range for the function. sirius charges $200 per year in addition to $50 per month for the first 3 months to receive its broadcast.

Given : Fix amount charges = $200.

Each month additional charge = $50.

Let us assume number of months are taken by x.

So, we can setup a function as

Total charge  = Fix charge + each month charge * number of months.

f(x)  = 200 + 50*x

Or f(x) = 200 +5x.

Where function f is the total charge of x number of months.

The values of x's represents domain and function value represents range.

According to problem, it is said " first three months".

So, we need to take number of months as x=0,1,2,3.

And we need to find values of function for those x values.

On plugging x=0,1,2 and 3 we would get

f(0) = 200 +5(0) = 200 +0 = 200.

f(1) = 200 +5(1) = 200 +50 = 250.

f(2) = 200 +5(2) = 200 +100 = 300.

f(3) = 200 +5(3) = 200 +150 = 350.

We got function values 200,250,300 and 350.

Therefore, with respect to the given situation, the domain of the funtion is

{0,1,2,3} and Range { 200,250,300, 350}.