Graph B was stretched vertically by a factor of 2 to obtain graph P.
Transformation from graph B to graph P:
The transformation from the graph of B(M) to the graph of P(M) is a vertical stretch by a factor of 2.
Here's why:
Function representation:
B(M) = 5M represents the cost of the basic service, where B is the cost in dollars and M is the number of months.
P(M) = 10M represents the cost of the premium service, where P is the cost in dollars and M is the number of months.
Cost factor:
The cost of the premium service is double the cost of the basic service for the same number of months. This means the graph of P(M) will be higher than the graph of B(M) by a constant factor of 2.
Transformation type:
Since the difference in cost is constant, vertically stretching the graph of B(M) by a factor of 2 will result in the graph of P(M).
Visual explanation:
Imagine the graph of B(M) plotted on a coordinate plane. Every point on the graph represents several months (M) and its corresponding cost (B) for the basic service.
To obtain the graph of P(M), we take every point on the graph of B(M) and double its y-coordinate (cost). This essentially stretches the graph vertically upwards by a factor of 2.
Therefore, the transformation from graph B to graph P is a vertical stretch by a factor of 2.