2. describe how the function g(x)= -3e^x - 1 - 5 was transformed from the graph of its parent function…

2. describe how the function g(x)= -3e^x - 1 - 5 was transformed from the graph of its parent function f(x)=e^x.

2. describe how the function g(x)= -3e^x - 1 - 5 was transformed from the graph of its parent function f(x)=e^x.

Answer

Explanation:

Step1: Analyze vertical stretch and reflection

The coefficient -3 in front of $e^{x - 1}$ causes a vertical stretch by a factor of 3 and a reflection across the x - axis.

Step2: Analyze horizontal shift

The $x-1$ inside the exponential function causes a horizontal shift 1 unit to the right.

Step3: Analyze vertical shift

The - 5 at the end of the function causes a vertical shift 5 units down.

Answer:

The graph of $f(x)=e^{x}$ is vertically stretched by a factor of 3, reflected across the x - axis, shifted 1 unit to the right and 5 units down to get the graph of $g(x)=-3e^{x - 1}-5$.