Tamara has decided to start saving for spending money for her first year of college. Her money is currently in a large suitcase under her bed, modeled by the function S(x) = 450. She is able to babysit to earn extra money and that function would be a(x) = 6(x - 2), where x is measured in hours. Explain to Tamara how she can

create a function that combines the two, and describe any simplification that can be done.

She can create a function for the total savings in terms of the time x by adding the two functions together. The new function should look like this:

T(x)=S(x)+a(x)

So now we can substitute the given functions:

T(x)=450+6(x-2)

But this function can be simplified for it to be easier for her to calculate her total amount of savings. We can do that by distributing the 6 into the parenthesis. This is, multiply the 6 by both the x and the -2, so we get:

T(x)=450+6x-12

and now we can combine like terms. We can subtract 12 from 450 so we get:

T(x)=6x+438

And that will be our final function.