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}
$