Final answer:
The question requires understanding of horizontal shifts in functions to determine the relationship between g(x) and f(x). The correct function representation depends on the type of transformation - vertical shifts, scaling, or horizontal shifts. Usually, g(x) = f(x - d) denotes a shift d units to the right, while g(x) = f(x + d) denotes a shift d units to the left.
Step-by-step explanation:
The question at hand involves using function notation to write a function g in terms of another function f(x). By understanding the concept of horizontal shifts in functions, we can determine how g(x) relates to f(x). Specifically, f(x + d) represents a function that is shifted d units to the left along the x-axis. The options provided suggest different types of transformations of f(x), including vertical shifts and scaling.
Using the given information about function transformation:
- If g(x) equals f(x) shifted 6 units up, the correct representation would be g(x) = f(x) + 6.
- If g(x) equals f(x) shifted 6 units down, the correct representation would be g(x) = f(x) - 6.
- If g(x) represents f(x) scaled by a factor of 6, then g(x) = 6f(x).
- If g(x) is f(x) shifted 6 units to the right, the expression would be g(x) = f(x + 6).
Without additional context or a graph to indicate the specific transformation, any of these options could potentially describe how g is written in terms of f(F). However, given the algebraic principle that addition inside the function argument shifts the graph to the left, g(x) = f(x + 6) should not be the correct answer if g is intended to represent a horizontal shift to the right.