Question

What is the piecewise-defined function that expresses the cost of the order, C(x), in terms of the number of photos ordered, x?

Answer 1

See below

Explanation:

The values in the table change by $3.80 from one line to the next. Since each change from line to line changes in number of photos by 20, the average cost per photo is $3.80/20 = $0.19. There is apparently a $5.80 -3.80 = $2.00 shipping charge for numbers of photos in the range shown in the table.

Thus, the piecewise function has 3 pieces:

for x < 100: $2.00 + 0.19x

for x < 200: $4.50 + 0.17x

for x ≥ 200: $0.15x

This could be written as ...

`C(x)=\left\{\begin{array}{rcl}\$2.00+0.19x&\text{for}&0\le x<100\\\$4.50+0.17x&\text{for}&100\le x<200\\\$0.15x&\text{for}&x\ge 200\end{array}\right.`