The problem shows two functions:

$f(x) = 2^x$ and $g(x) = 2^x - 3$

The question asks which transformation maps $f(x)$ onto $g(x)$.

Solution:

We can see that $g(x)$ is the same as $f(x)$ but shifted down by 3 units. This is because the term $-3$ subtracts 3 from the value of $f(x)$, which means the whole graph of $f(x)$ is shifted downward by 3 units.

Thus, the correct answer is:

• A shift down 3

Would you like a detailed explanation of function transformations, or do you have any questions?

Related Questions:

1. What is a vertical shift in function transformations?
2. How does adding or subtracting constants to functions affect their graphs?
3. Can a function be shifted both vertically and horizontally at the same time?
4. What does a horizontal shift look like for exponential functions?
5. How would the transformation change if the term were $+3$ instead of $-3$?

Tip:

When analyzing transformations, focus on how constants added or subtracted inside or outside the function affect its graph.