what would be the function be if 4^x if shifted 6 units to the left

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 \( f(x) \).

what would the function be if 4^x is shifted 6 units to the left

Understand how to shift the exponential function f(x) = 4^x by 6 units to the left. Learn about function transformations, specifically horizontal shifts, and how they impact the input of a function. This explanation includes step-by-step details suitable for students in Grades 10-12.

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