Question

1. the following function $f(x)=e^{x}$ was transformed to form $g(x)=2e^{x-3}-7$.

the graph of $f(x)$ was - choose the correct answer - by a factor of 2, shifted 3 units - choose the correct answer - , and shifted 7 units - choose the correct answer - to create the graph of $g(x)$.
clear all

Explanation:

Step1: Identify vertical scaling factor

The coefficient of $e^{x-3}$ is 2, so the graph of $f(x)=e^x$ is vertically stretched by a factor of 2.

Step2: Identify horizontal shift

The exponent is $x-3$, so the graph is shifted 3 units to the right.

Step3: Identify vertical shift

The term $-7$ at the end means the graph is shifted 7 units down.

Answer:

The graph of $f(x)$ was vertically stretched by a factor of 2, shifted 3 units to the right, and shifted 7 units down to create the graph of $g(x)$.