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# Functions

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280
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The graph of \$y=f(x)\$ is shown in red below. For how many values of \$c\$ is \$f(c) = -1\$?

[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 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(0.22),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(-6,5,-5,9);
real f(real x) {return ((x+4)*(x+1)*(x-1)*(x-3))/10;}
draw(graph(f,-4.5,3.5,operator ..), red);
[/asy]

(Assume grid lines are spaced 1 unit apart.)

Jul 20, 2022

#1
+1164
+8

OH MY GOD! DID YOU KNOW I DON'T READ JIBBERISH???!!!

Can you just upload the picture and not copy and paste the latex or whatever???

Jul 20, 2022
#2
+129800
+2

Yep...I agree, nerdiest  !!!!

CPhill  Jul 20, 2022