Final answer:
The resulting function after vertically stretching y = ex by a factor of 2, reflecting it across the x-axis, and shifting it down 3 units is y = -2ex - 3.
Step-by-step explanation:
The original function is y = ex. To find the resulting function after the described transformations (vertically stretched by a factor of 2, reflected across the x-axis, and shifted down 3 units), we perform each transformation step by step.
- Vertical Stretch: Multiplying the function by 2 gives us 2ex.
- Reflection across the x-axis: Multiplying by -1 to reflect it gives us -2ex.
- Shift down by 3 units: Subtracting 3 from the function gives us -2ex - 3.
Therefore, the resulting function after all transformations is y = -2ex - 3.