Question

A flat fee of $15.25 plus $3.45 per pound of supplies ordered is added to the bill to cover the shipping cost.The teacher budgets $49.75 for the shipping cost.Which list of values best represents the entire domain for shipping, f(x), as a function of the number of whole pounds of school supplies the teacher can order, x?

Answer 1

The domain of a function is the set of possible input value, the function can take.

The domain is [0,10]

The given parameters are:

$Flat\ Fee = 15.25$

$Rate = 3.45$

So, the function f(x) is:

$f(x) = Flat\ Fee + Rate \times x$

$f(x) = 15.25 + 3.45 \times x$

$f(x) = 15.25 + 3.45x$

Because x represents the number of orders, the value of x cannot be negative.

The teacher budgets $49.75.

This means that: f(x) = 49.75

So, we have:

$49.75 = 15.25 + 3.45x$

Collect like terms

$49.75 - 15.25 = 3.45x$

$34.5 = 3.45x$

Divide both sides by 3.45

$10 = x$

Rewrite as

$x = 10$

Hence, the domain is [0,10]

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