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 any job over 150 square feet.

a) Create a piecewise model to express the cost, C, of refinishing a floor as a function of the number of square feet, s, to be refinished.
b) Graph the function. Be sure to label your axis and use an appropriate scale.
c) Give the domain and range.

Answer 1

a) We have to express C=f(s) I.e. C which is cost of refinishing a floor as a function of s which is number of square feet to be refinished.

The word problem can be written mathematically as ,

cost of refinishing 1 square foot = $1.83  

number of square feet to be refinished =s

Thus, cost of refinishing s square feet = $ (1.83s) where

I.e. .......(i)

Now the second condition is that for any job over 150 square feet , additional charge of $350 is also taken.In other words,

.....(ii)

(I) and (ii) can be combined as

...(iii)

Now, additional amount is added only when job is over 150 feet, that is not when less than 150 thus, ...(iv)

Hence our piecewise defined function is

  

b)  

c) From the graph it is clear that Domain of f(s)( the permissible values of s) is   

Also the range ( the output C) can be seen as

• take reflection of the graph on C - axis and that gives us the range I.e. it is clearly union of two intervals [0,274.4] U (624.5, 2180]  

• Open circle is because the value at x=150 is given by C=1.83s and not the other one.

​​​​​Any doubts, feel free to comment.

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