Given the graph of $f$ , describe how the graph of $y = - f ( 2 x ) + 2$ can be obtained from the graph of $f$
A) Stretch horizontally by a factor of $2$ , then reflecting about the
$y$ - axis, then shifting
$2$ units up
B) Shrink vertically by a factor of $2$ , then reflecting about the
$x$ - axis, then shifting
$2$ units up.
C) Stretch horizontally by a factor of $2$ , then reflecting about the
$y$ - axis, then shifting
$2$ units up .
D) Shrink vertically by a factor of $\frac { 1 } { 2 }$ , then reflecting about the
$x$ - axis, then shifting downward
$2$ units.
E) Shrink horizontally by a factor of $\frac { 1 } { 2 }$ , then reflecting about the
$x$ - axis, then shifting
$2$ units up

Question

Quizplus · Accepted Answer

The transformation $y = -f(2x) + 2$ involves three steps: first, shrinking horizontally by a factor of $\frac{1}{2}$ due to the $2x$ inside the function (which compresses the graph horizontally), then reflecting about the $x$-axis because of the negative sign in front of $f$, and finally shifting the graph $2$ units up due to the $+2$ outside the function.

Given the Graph Of fff , Describe How the Graph Of y=−f(2x)+2y = - f ( 2 x ) + 2y=−f(2x)+2

Given the Graph Of $f$ , Describe How the Graph Of $y = - f ( 2 x ) + 2$