Final answer:
The transformation from f(x) to g(x) is a horizontal shift to the left by 2 units. Substituting x+2 into f(x), we find g(x) = 2x + 5. When graphing, both functions have the same slope but different y-intercepts, and the x-axis should be scaled up to 20.
Step-by-step explanation:
The transformation from f to g involves a horizontal shift of the graph of f(x) = 2x + 1. Specifically, the function g(x) = f(x + 2) represents a horizontal shift to the left by 2 units. To find the new equation for g(x), substitute x + 2 into f(x) giving us g(x) = 2(x + 2) + 1 which simplifies to g(x) = 2x + 5. If we graph both f(x) and g(x), we'll have two lines with the same slope but different y-intercepts. The graph of f(x) will cross the y-axis at 1, and the graph of g(x) will cross at 5, both with a slope of 2.
Labeling the graph with f(x) and x, you would scale the x and y axes in accordance with the functions' maximum values over the given domain. Since the linear functions continuously increase, no maximum value for y needs to be set beyond the scale of the graph. For x, you would at least need to go up to 20 to cover the given range for f(x).