Question Type 3: Given a description of transformations, finding the appropriate transformed function Bootcamps

Given $f(x)=e^x$, translate left 3 units, then apply a vertical stretch by 5, and then translate down 2 units. Find the new function.

Given $f(x)=x^2+1$, reflect in the $x$-axis, then shift right 2 units, and then translate up 4 units. Write the resulting function.

Given $f(x)=x^3$, apply a vertical stretch by factor 4, then a horizontal compression by factor 3, and then translate down 2 units. Find the final function.

Given $f(x)=\sin x$, horizontally stretch by a factor of 2, then translate up 1 unit, and finally reflect in the $y$-axis. Write the transformed function.

Given $f(x)=\sqrt{x-2}$, apply a vertical compression by factor $\tfrac13$, then translate up 6 units, and then shift left 1 unit. Find the transformed function.

Given $f(x)=|x+1|$, apply a horizontal compression by factor 2, then shift right 3 units, and finally apply a vertical stretch by factor 2. Write the new function.

Given $f(x)=\ln x$, reflect in the $y$-axis, then shift right 2 units, and then apply a vertical stretch by factor 3. Write the transformed function.

Given $f(x)=\tfrac{1}{x+2}$, reflect in the $x$-axis, then apply a horizontal compression by factor 4, shift right 1 unit, and translate up 3 units. Find the resulting function.