To determine the equation of the graph when [tex]\(f(x) = 4^x\)[/tex] is shifted 7 units to the left, we need to understand how horizontal shifts affect the equation of a function.
1. Horizontal Shift Basic Rule:
- If a function [tex]\( f(x) \)[/tex] is shifted to the left by [tex]\( h \)[/tex] units, the new function will be [tex]\( g(x) = f(x + h) \)[/tex].
2. Applying the Rule:
- Here, the original function is [tex]\( f(x) = 4^x \)[/tex].
- The graph is shifted 7 units to the left. Hence, [tex]\( h = 7 \)[/tex].
3. Forming the New Equation:
- Substituting [tex]\( h = 7 \)[/tex] into the shift rule, the new function becomes:
[tex]\[
g(x) = 4^{(x + 7)}
\][/tex]
Therefore, the correct answer is:
[tex]\[ \text{D. } g(x) = 4^{(x + 7)} \][/tex]
