question 4 (1 point)\nwhat transformations take the graph of f(x)=e^x to f(x)= -e^x - 2?
question 4 (1 point)\nwhat transformations take the graph of f(x)=e^x to f(x)= -e^x - 2?
Answer
Explanation:
Step1: Analyze the negative sign in front of $e^x$
The negative sign in $-e^x$ reflects the graph of $y = e^x$ about the $x$-axis. When we have $y = -f(x)$ for a function $y = f(x)$, all the $y$-values of the original function are multiplied by - 1.
Step2: Analyze the subtraction of 2
The subtraction of 2 in $-e^x-2$ shifts the graph of $y=-e^x$ downward by 2 units. For a function $y = f(x)$, the transformation $y=f(x)-k$ ($k>0$) shifts the graph of $y = f(x)$ downward by $k$ units.
Answer:
The graph of $y = e^x$ is reflected about the $x$-axis and then shifted downward by 2 units.