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consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.

the graph g(x) is the graph of f(x) translated (5, 3, 2) units (down, left, up, right) , and g(x) = f(x)+3, f(x)+2, f(x)-5 f(x-2) f(x-3) f(x+5)

Translation of 2 units to the right

g(x) = f(x-2)

Step-by-step explanation:

Given the original function , we can get the function plotted by translating the graph 2 units to the right.

As seen in the attached image, the original function f(x) is shown in orange, while the translation 2 units to the right is the function in blue. Notice that in the original function the crossing of the x-axis occurs at x = -1/3, and translating the function to the right 2 units moves the crossing two full units to the right, making it now cross the x-axis at x = 5/3

Such translation in 2 units to the right corresponds to a subtraction of 2 units from the x-variable in the original functional expression:

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step-by-step explanation: