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.

t(x) = 6x + 438

Step-by-step explanation:

The total (marked it as t) amount of money that Tamara has is the sum of the money under her bed and the money that she makes by babysitting.

Note that the first function is fixed and doesn't  actually depend on x (it could be written s = 450), so the only variable, which changes, is the hours (x) in the second function.

// combining the two functions

t(x) = 450 + 6(x − 2)

// simplification

t(x) = 450 + 6x − 12

t(x) = 450 + 6x − 12

// the simplified function is

t(x) = 6x + 438

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