Question

A floor refinishing company charges $1.73 per square foot to strip and refinish a tile floor for up to 1000 square feet. There is an additional charge of $375 for toxic waste disposal for any job which includes more than 150 square feet of tile.

(a) Find an equation for the amount C (in dollars) they will charge to refinish a floor which is x square feet when x≤150.

(b) Find an equation for the amount C (in dollars) they will charge to refinish a floor which is x square feet when x>150.

(c) Sketch a graph of the function y=C(x) on a separate piece of paper.

(d) Based on your graph and formulas from parts (a) and (b), what is the domain of C(x)?

(e) Based on your graph and formulas from parts (a) and (b), what is the range of C(x)?

Answer 1

(a) for x 150, C(x)= 1.73 x

(b) for x 150, C(x)= 375 + 1.73 x

(c) for x = 150, C(x) = 1.73(150)= 259.5. The graph would be straight line starting at the origin (0,0) and ending at point (150, 259.5)

for x 150 and up to x=1000, graph of C(x) would be as follows (rough sketch)

The cost of refinishing 100 sq ft would be $2105. Cost of refinishing area just exceeding 150 sqft would be $634.5

Domain of C(x) in the first case is closed interval [0,150] In the second case the domain would be (150, 1000] because the charges are for area not exceeding 1000 sq ft.

The range in the first case is 0 to 259.5 and in the second case it is 634,5 t0 2105

[ Domain and Range has been seperately given , because it is a piecewise function]

*****