Question 1177625



{{{f(x) = x^2}}} compressed horizontally by a factor of {{{1/2}}} is 

{{{g(x) =f (hx) }}}

if {{{0<h<1}}} the graph is stretched horizontally  by a factor {{{1/h}}}
if {{{h>1}}} the graph is compressed horizontally  by a factor {{{1/h}}}

in your case

{{{h=1/2 }}}=>compressed horizontally  by a factor {{{1/h=1/(1/2)=2}}}

{{{g(x) =(2x)^2}}}

reflecting it over the {{{y}}}-axis:

The graph is reflected about the y-axis when {{{f(x)=f(-x)}}}.
Reflecting this function across the y-axis, we replace {{{x}}} by {{{-x}}}. Hence, the reflection across the {{{y}}}-axis is {{{f(-x)=(-x)^2=x^2}}}, nothing changes

Therefore, the reflection is the {{{same}}} as the original function.


 {{{g(x) =(-2x)^2}}}



{{{ graph( 600, 600, -10, 10, -10, 10, x^2, (-2x)^2) }}}