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.

Add both of the function together.

Step-by-step explanation:

s(x) + a(x) = 450 + 6(x - 2)

1) The function that represents how the money in her suit case is s(x) = 450

The function that represents the amount she is able to make from baby sitting is a(x) = 6(x - 2)

Given that the values of the two function are the same units, dollars, and the amount are to be put to the same use for spending money for her first year of college, the combination of the two functions is the sum of their values given as follows;

f(x) = s(x) + a(x) = 450 + 6(x - 2)

2) For simplification, we expand the second term and add the constant terms as follows;

f(x) = 450 + 6·x - 12

f(x) = 450 + 6·x - 12

f(x) = 438 + 6·x

The sum of the two terms becomes, f(x) = 438 + 6·x

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step-by-step explanation: