Question

The function f(x) = 1,575 - 225x models the value of a computer x years after it was purchased. What is an appropriate domain for this function?

Answer 1

x = 0 is the smallest x can be. Anything smaller and it wouldn't make any sense because negative time values make no sense.

x = 7 is the largest x can be. Why? Because plugging in x = 7 leads to
f(x) = 1575 - 225x
f(7) = 1575 - 225*7
f(7) = 1575 - 1575
f(7) = 0
so at year 7, the value is 0 dollars. Any x value larger than 7 will produce negative dollar values, which make no sense.

Another way to get x = 7 is to notice that 1575 - 225x = 0 has the solution x = 7
We'd solve for x like so
1575 - 225x = 0
1575 = 225x
225x = 1575
x = 1575/225
x = 7


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So x = 0 is the smallest x can be and x = 7 is the largest x can be. This means the domain is
`0 \le x \le 7`

Answer: Choice D