Question

the carpenter’s chronicle charges $12 for each of the first three lines of a classified ad and $7.25 for each additional line. Express the cost of an x-line ad, c(x), algebraically as a piecewise function.

Answer 1

c(x) = (12x I 1 < = x < = 3

36 + 7.25x I x> 3)

Answer 2

The required piecewise function is

`C(x)=\begin{cases}12x & \text{ if } 0\leq x\leq 3 \\ 36+7.25x & \text{ if } x>3 \end{cases}`

Explanation:

It is given that the carpenter’s chronicle charges $12 for each of the first three lines of a classified ad.

For 0 ≤ x ≤ 3, the cost function is

`C(x)=12x`

Carpenter’s chronicle charges $7.25 for each additional line after 3 lines.

For x > 3, the cost function is

`C(x)=12(3)+7.25x`

`C(x)=36+7.25x`

Therefore the required piecewise function is

`C(x)=\begin{cases}12x & \text{ if } 0\leq x\leq 3 \\ 36+7.25x & \text{ if } x>3 \end{cases}`