Question

The function f(x) = 3x^2 models the packaging costs, in cents, for a box shaped like a rectangular prism. The side lengths are 4x ft, 5x ft, and 6x ft. What are reasonable domain and range values for this function, if the longest side length of the box can be no greater than 90 ft?

Answer 1

Answer:

$0 < x < 15, 0 < f(x) < 675$

Step-by-step explanation:

The value of x associated with maximum allowable length is:

$x_{max} = \frac{90\,ft}{6}$

$x_{max} = 15$

The maximum packaging cost is:

$f(x_{max})= 3\cdot (15)^{2}$

$f(x_{max}) = 675\,cents$

The domain and range values for this function are, respectively:

$0 < x < 15, 0 < f(x) < 675$