Question

help asap pls due today The graph of $y = f(x)$ is shown below. Assume the domain of $f$ is $[-4,4]$ and that the vertical spacing of grid lines is the same as the horizontal spacing of grid lines. [asy] size(150); real ticklen=3; real tickspace=2; real ticklength=0.1cm; real axisarrowsize=0.14cm; pen axispen=black+1.3bp; real vectorarrowsize=0.2cm; real tickdown=-0.5; real tickdownlength=-0.15inch; real tickdownbase=0.3; real wholetickdown=tickdown; void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) { import graph; real i; if(complexplane) { label("$\textnormal{Re}$",(xright,0),SE); label("$\textnormal{Im}$",(0,ytop),NW); } else { label("$x$",(xright+0.4,-0.5)); label("$y$",(-0.5,ytop+0.2)); } ylimits(ybottom,ytop); xlimits( xleft, xright); real[] TicksArrx,TicksArry; for(i=xleft+xstep; i 0.1) { TicksArrx.push(i); } } for(i=ybottom+ystep; i 0.1) { TicksArry.push(i); } } if(usegrid) { xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);//,above=true); yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.22),extend=true), p=invisible);//,Arrows); } if(useticks) { xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize)); yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize)); } else { xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize)); yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize)); } }; rr_cartesian_axes(-5,5,-5,6); draw((-4,4)--(-1,0)--(0,2)--(4,-4),red); [/asy] Part (a): The points $(a,4)$ and $(b,-4)$ are on the graph of $y = f\left( 2x \right).$ Find $a$ and $b.$ Part (b): Find the graph of $y = f\left( 2x \right).$ Verify that your points from part (a) are on the graph. Part (c): The points $(c,4)$ and $(d,-4)$ are on the graph of $y = f\left( 2x - 8 \right).$ Find $c$ and $d.$ Part (d): Find the graph of $y = f\left( 2x - 8 \right).$ Be sure to verify that your points from part (c) are on the graph both algebraically and geometrically. This week, it is important that your submission includes graphs.

Answer 1

Answer:

Wht..............................................................

Answer 2

Answer:

( 1, 3 )

Step-by-step explanation:

If the graphs intersect at ( a , b ) then,

$h(a) = h(a-3) = b.$

So,

$(a,b)$ and $(a-3,b)$ are both on the original graph of $y=h(x)$. Looking for two points on the original graph which are separated by 3 units horizontally, we find $(-2,3)$ and $(1,3)$.  So $a-3=-2,$ $a=1,$ and $b=3;$ the graphs of $y=h(x)$ and $y=h(x-3)$ intersect at :

$\boxed{(1,3)} .$

Next time, please try to insert a picture of the graph.

This problem is difficult, so feel free to ask questions. : )

Reference :

Parabolas ; $y = a( x - h ) ^2 + k$