A videoke machine can be rented for 1, 000 pesos for three days, but for the fourth day onwards, an additional cost of 400 pesos per day is added. Represent the cost of renting a videoke machine as piecewise function of the number of days it is rented and plot its graph.

1000+400d if d>3

Yes

C=1000+1400n

To represent the cost of renting a videoke machine as a piecewise function, we can define two separate functions based on different conditions.

Let's assume:
- x = the number of days the videoke machine is rented
- C(x) = the cost of renting the videoke machine for x days

Now let's define the piecewise function:

For x ≤ 3 (first three days):
C(x) = 1000 pesos (constant cost for the first three days)

For x > 3 (fourth day onwards):
C(x) = 1000 + (x - 3) * 400 pesos (additional 400 pesos per day)

To plot this piecewise function on a graph, we will represent the number of days (x) on the x-axis and the cost (C) on the y-axis.

Let's assume the range of x to be from 0 to 7 for better visualization.

Now, let's calculate the cost for each condition:

- For x ≤ 3:
When x = 0, C(x) = 1000 pesos
When x = 1, C(x) = 1000 pesos
When x = 2, C(x) = 1000 pesos
When x = 3, C(x) = 1000 pesos

- For x > 3:
When x = 4, C(x) = 1000 + (4 - 3) * 400 pesos = 1400 pesos
When x = 5, C(x) = 1000 + (5 - 3) * 400 pesos = 1800 pesos
When x = 6, C(x) = 1000 + (6 - 3) * 400 pesos = 2200 pesos
When x = 7, C(x) = 1000 + (7 - 3) * 400 pesos = 2600 pesos

Now, let's plot the graph with the above information:

For x ≤ 3:
- Draw a horizontal line at y = 1000 pesos for x ≤ 3.

For x > 3:
- Plot the points (4, 1400), (5, 1800), (6, 2200), and (7, 2600) and draw a line connecting these points.

The resulting graph will show a horizontal line at y = 1000 pesos for the first three days, and then a linearly increasing line from day four onwards with a slope of 400 pesos per day.

Note: The graph provided here is a basic visual representation and may not be to scale.