Answer:
The piece-wise function is;
[tex]f\left (x \right ) = \begin{cases} \$ 45 \times x & \text{ if } x \leq 3 \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}[/tex]
Step-by-step explanation:
The flat rate for renting the car = $35 per day
The amount charged as insurance fee per day for renting the car for 3 days or less = $10
The insurance fee charged per day when the car is rented for more than 3 days = $5
Let the number of days = x
Therefore, we have;
For x ≤ 3, f(x) = 35 × x + 10 × x = x × (35+10) = 45·x
For x > 3, f(x) = 35 × x + 5 × x = x × (35+5) = 40·x
Therefore;
The charge rate for renting the car for less than or equal to 3 days = 45·x
The charge rate for renting the car for more than 3 days = 40·x
The piece-wise function can be presented as follows;
[tex]f\left (x \right ) = \begin{cases} \$ 45 \times x & \text{ if } x \leq 3 \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}[/tex]
