The parent function of \( f(x) = 14 \cdot 3^{x+5} + 8 \) is the exponential function \( g(x) = 3^x \). The function undergoes several transformations:
- Horizontal Shift: The term \( x + 5 \) indicates a horizontal shift to the left by 5 units.
- Vertical Stretch: The coefficient \( 14 \) in front of \( 3^{x+5} \) means the graph is vertically stretched by a factor of 14, making it grow faster than the parent function.
- Vertical Shift: The addition of \( 8 \) at the end moves the entire graph upwards by 8 units.
Combining these transformations, the graph of \( f(x) \) is first shifted left by 5 units, then stretched vertically by 14, and finally moved up by 8 units.