Question

The total cost of a purchase of a number ofChromebooks, x can be represented by the functionc(x) = 250x. Which set of numbers best defines thedomain of c(x)? Explain how you know.A: integersB: Positive IntegersC: Rational NumbersD: Positive Rational Numbers

Answer 1

The Answer is Positive Integers (B)

The number of Chromebooks = x

The total cost of purchasing Chromebooks = c(x)

where x is the domain of c(x)

The number of Chromebooks x can be: {0, 1, 2, 3, 4, 5, 6...}. You cannot have numbers like {0.2, 0.5, 3.8 ...} or any other decimal neither can you have surds like:

`\sqrt[]{3},\sqrt[]{8},\sqrt[]{55},\text{ and so on}`

Integers contain numbers like: {... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...}

Positive Integer contains numbers like: {1, 2, 3, 4, 5, ...}

Rational Numbers contain numbers like: {-0.2, -0.1, -0.05, -0.005,0.2, 0.1, 0.05, 0.005,...} and also contain numbers like {... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...} as in Integers.

Positive rational Numbers are just the positive values of Rational Numbers like: {1, 2, 3, 4, 5, ...} and {0.2, 0.1, 0.05, 0.005,...}

From the information laid out, it is obvious that the only set of values that qualify to be called the domain of c(x) is Positive Integers

The Answer is Positive Integers (B)