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The graph of  is shown below, in red. Find the equation that corresponds to the blue graph.
[asy]
size(180);

real f(real x) {
real y;

if (x >= -4 && x <= -1) {y = -5/3*(x + 1) - 1;}
if (x >= -1 && x <= 0) {y = 4*(x + 1) - 1;}
if (x >= 0 && x <= 4) {y = -1/2*x + 3;}

return (y);
}

real g(real x) {
return (f(x + 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 if(abs(i) >0.1) {
TicksArrx.push(i);
}
}
for(i=ybottom+ystep; i if(abs(i) >0.1) {
TicksArry.push(i);
}
}

if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.72),extend=true),p=invisible);//,above=true);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.72),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(-7,7,-7,7);

draw(graph(f,-4,4),red+1.125bp);
draw(graph(g,-6,2),blue+1.125bp);

label("$y = f(x)$", (6,2), UnFill);
[/asy]


Enter your answer in the form y=..

 May 7, 2023
 #1
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0

The answer is "y = f(3x - 2) + 1".

 May 8, 2023

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