To understand the effect of the function g(x) = |3x| + 1, we need to compare it with the original function f(x) = 3x.The absolute value function |3x| takes any negative input value and makes it positive, so it reflects the left half of the graph of f(x) across the x-axis. This means that the graph of g(x) will have the same shape as f(x) for positive x-values, but will be reflected across the x-axis for negative x-values.Additionally, the function g(x) adds 1 to the output of |3x|, so the entire graph of g(x) is shifted up by 1 unit.Therefore, the correct answer is C. The graph of g(x) is compressed horizontally (due to the absolute value function) and shifted up 1 unit.