Task 262

The task

Below is a portion of the graph of a function, $y=E(x)$: [asy] import graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-4.5,xmax=4.5,ymin=-0.99,ymax=6.5; pen cqcqcq=rgb(0.75,0.75,0.75); /*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("2 2"); real gx=1,gy=1; for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs); Label laxis; laxis.p=fontsize(10); xaxis("",xmin,xmax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true); yaxis("",ymin,ymax,Ticks(laxis,Step=1.0,Size=2,NoZero),Arrows(6),above=true); real f1(real x){return sqrt(abs(x+1))+(9/pi)*atan(sqrt(abs(x)));} draw(graph(f1,xmin,xmax),linewidth(1)); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); label("$y=E(x)$",(xmax+0.25,f1(xmax)),E); [/asy] The value of $E(3)$ is an integer. What is it?