Final answer:
To transform a graph by compressing it by 1 and moving it right by 4, replace x with (x - 4) in the function's equation, resulting in g(x) = f(x - 4), since a compression by 1 is no change.
Step-by-step explanation:
To write a transformation on a graph that is compressed by 1 and moved to the right by 4, you would adjust the function's equation to reflect these changes. For a given function f(x), a compression by a factor of 1 is actually no change to the graph's vertical stretch or compression. However, to shift the graph to the right by 4 units, you would replace x with (x - 4). So, if we have a base function f(x), after the transformation, the new function g(x) would be represented as g(x) = f(x - 4).
For example, if the original function were f(x) = x^2, the transformed function after moving it to the right by 4 units would be g(x) = (x - 4)^2. To graph this, you would plot all the points of f(x) 4 units to the right for the corresponding values of x.