Final answer:
When the function () = 1 is replaced with 1 3 ( − 2), the graph will shift 2 units to the right and become narrower by a factor of 3 along the y-axis.
Step-by-step explanation:
When the function () = 1 is replaced with 1 3 ( − 2), it means that wherever there was 'x' in the function, we will now substitute it with '1 3 ( − 2)'.
So the new function becomes () = 1 3 ( − 2).
To understand the effect on the graph, we need to analyze the transformation of the original function.
In this case, the function has undergone a horizontal translation to the right by 2 units and a vertical compression by a factor of 3.
The key concept to remember is that horizontal translations affect the x-values and vertical compressions affect the y-values.
By substituting 'x' with '1 3 ( − 2)' in the original function, the graph will shift 2 units to the right and become narrower by a factor of 3 along the y-axis. The shape of the graph will remain the same, but its position and size will change according to these transformations. So therefore the graph will shift 2 units to the right and become narrower by a factor of 3 along the y-axis.