The question asks about the transformation between $f(x) = \ln(x)$ and $g(x) = \ln(x + 2)$.

Explanation:

The transformation between these two functions involves a horizontal shift:

• The function $f(x) = \ln(x)$ is shifted horizontally because the term inside the logarithm has changed from $x$ to $x + 2$.
• Adding 2 inside the function, i.e., $g(x) = \ln(x + 2)$, means that the graph of $f(x)$ is shifted to the left by 2 units. This is because $\ln(x + c)$ causes a shift to the left by $c$ units when $c > 0$.

Thus, the correct answer is:

• Shift 2 to the left.

Do you need any more details or have questions?

Here are some related questions to expand your understanding:

1. What transformation occurs when $f(x) = \ln(x)$ becomes $g(x) = \ln(x - 3)$?
2. How would you shift $f(x) = \ln(x)$ vertically?
3. What happens to the graph of $f(x) = \ln(x)$ if $g(x) = -\ln(x)$?
4. How do you reflect the graph of $f(x) = \ln(x)$ over the x-axis?
5. What kind of transformation would result in the equation $g(x) = \ln(2x)$?

Tip: Horizontal transformations inside a function affect the x-values, while vertical transformations (outside the function) affect the y-values.