To solve this problem, let's analyze the given function and the transformations:

Given Function:

$h(x) = 2^{x-1} - 2$

Parent Function:

The parent function is: $f(x) = 2^x$

Transformations:

The function $h(x)$ is derived from $f(x)$ by:

1. Horizontal Shift: The term $x-1$ in the exponent means the graph is shifted 1 unit to the right.
2. Vertical Shift: The term $-2$ at the end means the graph is shifted 2 units downward.

Correct Answer:

The correct option is: C. The graph of $f(x) = 2^x$ should be horizontally shifted 1 unit to the right and vertically shifted 2 units downward.

If you have further questions or need additional details, let me know!

Here are 5 related questions to expand understanding:

1. What is the domain and range of the function $h(x)$?
2. How does a horizontal shift affect the x-intercept of an exponential function?
3. What is the asymptote of $h(x)$ after these transformations?
4. How would the transformations differ if the function were $h(x) = 2^{x+1} - 2$?
5. How would you graph $h(x)$ without a graphing utility?

Tip: Always analyze the transformations step by step to ensure clarity in how they modify the parent function!