Final Answer:
The transformation of the graph of f(x)=[x] to the graph of g(x)=∣2x∣ involves a horizontal compression.option.c
Step-by-step explanation:
The function f(x)=[x] represents the greatest integer less than or equal to x. This function has a series of vertical line segments at each integer value of x, creating a step-like graph. On the other hand, the function g(x)=∣2x∣ represents the absolute value of 2x. This function results in a V-shaped graph with its vertex at the origin and slopes of 2 on either side of the y-axis. When comparing these two functions, it is evident that g(x)=∣2x∣ is a horizontally compressed version of f(x)=[x].
To understand this transformation, we can consider specific points on the graphs. For instance, when x=1, f(1)=1 and g(1)=2. Similarly, when x=0.5, f(0.5)=0 and g(0.5)=1. This shows that for every value of x, the corresponding value of g(x) is half that of f(x), indicating a horizontal compression by a factor of 2.
In summary, the transformation from f(x)=[x] to g(x)=∣2x∣ involves a horizontal compression by a factor of 2, as every point on the graph of g(x) is located at half the distance from the y-axis compared to its corresponding point on the graph of f(x)=[x].
correct option is c) Horizontal compression