1.12 Transformations of Functions

3 practice questions

Notes

From $f(x)$:

$f(x)+k$: shift up $k$. $f(x-h)$: shift right $h$.
$af(x)$: vertical stretch by $|a|$ (reflect over $x$-axis if $a<0$).
$f(bx)$: horizontal compression by $\displaystyle \frac{1}{|b|}$ (reflect over $y$-axis if $b<0$).

$g(x)=f(x+3)-2$ shifts $f$:

$g(x)=-f(x)$ is a reflection over the:

$g(x)=f(2x)$ is a: