James has decided to start saving for a cruise over the summer. His money is currently in the local bank, modeled by the function s(x) = 102. He is able to do work around the neighborhood to earn extra money and that function would be a(x) = 8(x + 2), where x is measured in hours. Explain to James how he can create a function that combines the two, and describe any simplification that can be done.

Solution

s(x) = 102

a(x) = 8(x+2)

let new function is f(x) , which is the combination of two functions s(x) and a(x)

f(x) = s(x) + a(x)

f(x) = 102 + 8(x+2)

f(x) = 102 +8x +16

f(x) = 8x + 118

So f(x) = 8x + 118 is the new combined function to tell the total money James currently have.