To solve this problem, we are asked to determine how the graph of $f(x) = \log_3 x$ is transformed to the graph of $h(x) = 7 + \log_3 x$.

Step-by-step Explanation:

1. Base Function: The function $f(x) = \log_3 x$ is the base graph.

2. Transformation in $h(x)$: The given function is $h(x) = 7 + \log_3 x$. The "+7" outside the logarithmic function indicates a vertical shift upward by 7 units.

3. Graphical Impact:

   • Adding 7 to the output of the function moves every point on the graph of $f(x)$ upward by 7 units.
   • The vertical asymptote (at $x = 0$) remains unchanged because vertical shifts do not affect the asymptote.

4. Correct Answer:

   • The correct transformation is "The graph of $f(x) = \log_3 x$ should be shifted 7 units upward."
   • This matches option B.

Would you like me to provide additional visualizations or further breakdowns of the transformations?

Related Questions:

1. What is the effect of adding or subtracting constants inside the logarithmic function?
2. How would a horizontal shift affect the vertical asymptote of $f(x) = \log_3 x$?
3. What happens to the domain and range of the function after this transformation?
4. Can you explain how a vertical stretch would transform $f(x) = \log_3 x$?
5. What are the steps to graph $f(x) = \log_3 (x - 2) + 5$?

Tip:

When interpreting transformations, remember:

• Changes outside the function (like "+7") affect the vertical position.
• Changes inside the function (like $x + c$) affect the horizontal position.