if the function y = e^(-3x) is vertically compressed by a factor of 4, reflected across the y - axis, and…

if the function y = e^(-3x) is vertically compressed by a factor of 4, reflected across the y - axis, and then shifted down 5 units, what is the resulting function? write your answer in the form y = ce^(ax)+b. provide your answer below: y =

if the function y = e^(-3x) is vertically compressed by a factor of 4, reflected across the y - axis, and then shifted down 5 units, what is the resulting function? write your answer in the form y = ce^(ax)+b. provide your answer below: y =

Answer

Explanation:

Step1: Vertical compression

When a function $y = f(x)$ is vertically compressed by a factor of $k$, the new - function is $y=\frac{1}{k}f(x)$. For $y = e^{-3x}$ compressed by a factor of $4$, the function becomes $y=\frac{1}{4}e^{-3x}$.

Step2: Reflection across the y - axis

When a function $y = f(x)$ is reflected across the $y$-axis, we replace $x$ with $-x$. So, $y=\frac{1}{4}e^{-3x}$ becomes $y = \frac{1}{4}e^{-3(-x)}=\frac{1}{4}e^{3x}$.

Step3: Vertical shift down

When a function $y = f(x)$ is shifted down by $h$ units, the new function is $y=f(x)-h$. For $y=\frac{1}{4}e^{3x}$ shifted down 5 units, the function becomes $y=\frac{1}{4}e^{3x}-5$.

Answer:

$y=\frac{1}{4}e^{3x}-5$