Piecewise functions are used to represent functions that have several domain intervals.
The difference between both ads is #9
The piecewise function is given as:
[tex]\mathbf{ f(x) = \left[\begin{array}{ccc}32& &x\le 3\\32 +9(x - 3)&\ &x >3\end{array}\right] }[/tex]
The complete question requires that, we calculate the difference in the cost of a 6-line ad and a 7-line ad.
When [tex]\mathbf{x = 6}[/tex]
We make use of:
[tex]\mathbf{f(x) = 32 + 9(x - 3)}[/tex] because [tex]\mathbf{ x > 3}[/tex] covers x = 6
So, we have:
[tex]\mathbf{f(6) = 32 + 9(6 - 3)}[/tex]
[tex]\mathbf{f(6) = 59}[/tex]
When [tex]\mathbf{x = 7}[/tex]
We make use of:
[tex]\mathbf{f(x) = 32 + 9(x - 3)}[/tex] because [tex]\mathbf{ x > 3}[/tex] covers x = 7
So, we have:
[tex]\mathbf{f(7) = 32 + 9(7 - 3)}[/tex]
[tex]\mathbf{f(7) = 68}[/tex]
The difference (d) is then calculated by subtracting f(6) from f(7)
[tex]\mathbf{d = f(7)-f(6)}[/tex]
[tex]\mathbf{d = 68 - 59}[/tex]
[tex]\mathbf{d = 9}[/tex]
The difference between both ads is #9
Read more about piecewise functions at:
https://brainly.com/question/12561612
