Single Variable Calculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 9

Describe how the graphs of the following functions can be obtained from the graph of $f$. Suppose that the graph of $f$ is given.



$\begin{equation} \begin{aligned} \text{a) } y=& f(x) + 8\\ & \text{ shift the graph 8 units upward}\\ \text{b) } y=& f(x+8)\\ & \text{ shift the graph 8 units to the left}\\ \text{c) } y=& 1+2f(x)\\ & \text{ stretch the graph vertically by a factor of 2, then shift it 1 unit upward}\\ \text{d) } y=& f(x-2) - 2\\ & \text{ shift the graph 2 units to the right and 2 units downward}\\ \text{e) } y=& -f(x)\\ & \text{ reflect the graph about the $x$-axis}\\ \text{f) } y=& 3-f(x)\\ & \text{ reflect the graph about the line $x$-axis, then shift it 3 units upward.} \end{aligned} \end{equation}$