Final answer:
The graph of g(x) = log₁₀(x+3) + 1 is shifted 3 units to the left and 1 unit up compared to the graph of f(x) = log₁₀(x).
Step-by-step explanation:
The statement that best describes the translation from f(x) = log₁₀(x) to g(x) = log₁₀(x+3) + 1 is that the curve of the function g(x) is shifted to the left by 3 units and up by 1 unit compared to the curve of the function f(x). To understand why, we first recognize that adding a number inside the logarithm function (e.g., x to x+3) shifts the graph horizontally in the opposite direction of the sign of the number added, meaning a shift of 3 units to the left in this case. Adding a constant outside the logarithm (e.g., from log₁₀(x) to log₁₀(x) + 1) shifts the graph vertically upwards by the value of the constant. This is because the input of the log function is not changed; only the output value of each input is increased by 1.