If the function $f(x) = 4^x$ is shifted 6 units to the left, the transformation will affect the input of the function. A horizontal shift to the left by 6 units is represented by replacing $x$ with $x + 6$.

Thus, the new function will be:

$f(x) = 4^{x+6}$

Explanation:

• Shifting left by 6 units means that every $x$-value in the original function occurs 6 units earlier, so we replace $x$ with $x + 6$ in the exponent.

Would you like more details or have any further questions?

Here are some related questions:

1. What would the function be if shifted 6 units to the right?
2. How would the graph of $f(x) = 4^x$ change if shifted vertically instead?
3. What happens if the function is reflected across the y-axis?
4. How does shifting affect the domain and range of $f(x) = 4^x$?
5. Can you explain the difference between horizontal and vertical transformations?

Tip: Horizontal shifts change the input $x$, while vertical shifts change the output $f(x)$.