Final answer:
The value of 'k' determines the horizontal stretch or compression of the function g(x) = f(kx). To find 'k', you must compare how the input 'x' values are scaled between g(x) and f(x).
Step-by-step explanation:
The student is asking about the transformation of functions, specifically, how a function g(x) is related to a function f(x) when g(x) = f(kx). Where k is a constant that stretches or compresses the graph of f(x) horizontally. To determine the value of k, one must look at how the input values ('x' values) for g(x) are scaled relative to f(x). If for every 'x' in g(x), you have to use a 'kx' in f(x) to get the same output, k is a horizontal stretch or compression factor.
If 'k' is greater than 1, the function is compressed horizontally; if 'k' is between 0 and 1, the function is stretched; and if 'k' is negative, there is also a reflection across the y-axis in addition to the horizontal stretch or compression. Without the specific graphs or additional information, the exact value of k cannot be determined, but the concept the student must master is how the transformations affect the graph of the function.