A videoke machine can be rented for 1000 pesos for 3 days but for the fourth day onwards an addition cost of 400 pesos per day I added. Represent the cost of renting a videoke machine as a piecewise function of the number of days it is rented and plot it's graph.
Please kindly answer this question. Thank you so much
To represent the cost of renting a videoke machine as a piecewise function, we need to define different cost formulas based on the number of days.
Let's say the number of days rented is represented by the variable "x". We can define the piecewise function as follows:
Cost (C) = 1000 pesos (for the first 3 days)
Cost (C) = 1000 + (x - 3) * 400 pesos (for the fourth day onwards)
To visualize this as a graph, we can plot the cost on the y-axis and the number of days rented on the x-axis.
Here's the graph:
```
|
1400 P | *
| *
1200 P | *
| *
1000 P | *
| *
800 P | *
| *
600 P | *
|_______________________
3 4 x
```
In the graph, the cost remains constant at 1000 pesos for the first three days (represented by the flat line segment), and then it increases by 400 pesos per day starting from the fourth day onwards (represented by the diagonal line segment).
To represent the cost of renting a videoke machine as a piecewise function, we need to break it down into two separate cases: one for the first three days of renting and another for the fourth day onwards.
For the first three days, the cost is a fixed amount of 1000 pesos for the entire duration. So the function can be represented as:
Cost(D) = 1000 pesos (for 1 ≤ D ≤ 3)
For the fourth day onwards, there is an additional cost of 400 pesos per day. In this case, the number of days rented will be greater than 3. So the function can be represented as:
Cost(D) = 1000 + 400(D - 3) pesos (for D > 3)
To plot the graph of this piecewise function, we can use a graphing calculator or create a table of values to plot the points. Let's assume D represents the number of days rented and C represents the cost in pesos.
Here's a table:
D | C
--------------
1 | 1000
2 | 1000
3 | 1000
4 | 1400
5 | 1800
6 | 2200
By plotting these points on a graph, we will have a step-like graph with a horizontal line at y = 1000 for the first 3 days and a linear increasing line starting at (4, 1400). The graph will have a break (or a hole) at (3, 1000) since the cost remains the same for the next day.
I hope this helps! Let me know if you have any further questions.