Question

A floor refinishing company charges $1.83 per square foot to strip and refinish a tile floor for up to 1000 square feet. There is an additional charge of $350 for toxic waste disposal for any job which includes more than 150 square feet of tile.

A) Express the cost, y, of refinishing a floor as a function of the number of square feet, x, to be refinished.
b) Graph the function, give the domain and range.

Answer 1

Here x represents the number of square feet to be refinished and y represents the cost of refinishing the floor,

Given,

The cost of a tile floor for up to 1000 square feet is $1.83 per square,

So, the cost of x square feet of tile = 1.83x for x ≤ 1000

⇒ y = 1.83x for x ≤ 1000

Since, there is an additional charge of $350 for toxic waste disposal for any job which includes more than 150 square feet of tile.

That is, y = 1.83x + 350, for x > 150

So, y must be 1.83x for x ≤ 150.

A) Hence, the function that express the cost, y, of refinishing a floor as a function of the number of square feet, x, to be refinished, is,

`y=\begin{cases}1.83x & \text{ if } 0\leq x\leq 150 \\ 1.83x+350 & \text{ if } 150< x\leq 1000\end{cases}-----(1)`

B) The domain of the function = all possible value of x

⇒ Domain = 0 ≤ x ≤ 1000

Range = All possible value of y,

Since, the range of function y=1.83x, 0≤ x ≤ 150 is [0, 274.5]

While the range of function y = 1.83x + 350, for x > 150 is (624.5, 2180]

Hence, the range of the function (1) = [0, 274.5]∪(624.5, 2180]