## Calculus 8th Edition

(a) $y=f(2x)$, in this case we have to shrink the graph of $f$ horizontally by a factor of 2. (b) $y=f(\frac{1}{2}x)$, stretch the graph of $f$ horizontally by a factor of 2. (c) $y=f(-x)$, reflect the graph of $f$ about the $y$-axis. (d) $y=-f(-x)$, reflect the graph of $f$ about both the $y$-axis and $x$-axis (in this case it doesn't matter which reflection will be done first; in both cases we will get the same graph).