Question 1203719
<pre>
Greenestamps has found an answer.  This is his piecewise function: 

{{{matrix(1,3,f(x),""="",system(
matrix(4,3,

x^2, for, x<=1,
sqrt(x), for, 1<x<=4,
x-2, for, 4<x<=5,
e^x+3-e^5, for, x>5)
))}}}
I'll draw the final graph of his answer.

Notice that his last part looks like a vertical line, but it is NOT!!
It is a very rapidly increasing exponential function. It increases
from (5,3) way up to the point (6,258+) and all the way to +infinity.

{{{drawing(400,400,-6,10,-6,10,

circle(1,1,0.06), circle(4,2,0.06), circle(5,3,0.06),

graph(400,400,-6,10,-6,10,x^2*sqrt(1-x)/sqrt(1-x) ),

graph(400,400,-6,10,-6,10,sqrt(x)*(  sqrt(1.5-abs(x-2.5))  )/(  sqrt(1.5-abs(x-2.5))  )),

graph(400,400,-6,10,-6,10,(x-2)*(  sqrt(0.5-abs(x-4.5))  )/(  sqrt(0.5-abs(x-4.5))  )),

graph(400,400,-6,10,-6,10,(e^x+3-e^5)*sqrt(x-5)/sqrt(x-5))

)}}}

Edwin</pre>