Chapter 1.2, Problem 10E

To determine

To transform: The given function according to the stated situation.

Answer to Problem 10E

Transformed function is $g(x)=4000x-12000$ and it will take $3$ weeks to pay off the extra expense.

Explanation of Solution

Given information: $f(x)=4000x$ , extra expense incurred is $\$12000$ .

Calculation:

As $x-axis$ represents the weeks and $y-axis$ represents the income, so an extra expense of $\$12000$ at the starting would mean that the income at starting point is $-12000$ instead of $0$ .

So, transformation should be $12000$ units down.

  $\begin{array}{l}g(x)=f(x)-12000\\ g(x)=4000x-12000\end{array}$

When all the extra expense is paid, then income will no longer remain negative and will become equal to $0$ .

So, putting $g(x)=0,$

  $\begin{array}{l}4000x-12000=0\\ x=\frac{12000}{4000}\\ x=3\end{array}$

Thus, transformed function is $g(x)=4000x-12000$ and it will take $3$ weeks to pay off the extra expense.