Question 668011
GRAPH THE PIECEWISE - DEFINED FUNCTION F(X)={-1/4 X SQUARED + 3 FOR X LESS THAN OR EQUAL TO 2 AND 1/4 X FOR X GREATER THAN 2}
<pre>

f(x) = {{{system(   

matrix(2,4,

expr(-1/4)x^2+3,"","", x<=2,
expr(1/4)x, "","",     x>2) ) }}}

Below is the full graph of y = {{{expr(-1/4)x^2+3}}}
and to the right is the graph with the part to the right
of x=2 chopped off and a solid darkened circle at the
endpoint at 2 since that point (2,2) IS included in the 
final graph of the piecewise function f(x)



{{{drawing(800/3,200,-6,10,-6,6,

graph(800/3,200,-6,10,-6,6,(-1/4)x^2+3)  )}}}{{{drawing(800/3,200,-6,10,-6,6,
circle(2,2,.2),circle(2,2,.15),circle(2,2,.13),circle(2,2,.1),
circle(2,2,.21),circle(2,2,.19),circle(2,2,.22),circle(2,2,.03),
circle(2,2,.2),circle(2,2,.15),circle(2,2,.13),circle(2,2,.1),
circle(2,2,.21),circle(2,2,.19),circle(2,2,.22),circle(2,2,.03),
graph(800/3,200,-6,10,-6,6,((-1/4)x^2+3)*sqrt(2-x)/sqrt(2-x)

)  )}}}

Below is the full graph of y = {{{expr(1/4)x}}}
and to the right is the graph with the part to the left
of x=2 chopped off and a open circle at the
endpoint at 2 since that point (2,{{{1/2}}}) IS NOT included in the 
final graph of the piecewise function f(x).

{{{drawing(800/3,200,-6,10,-6,6,

graph(800/3,200,-6,10,-6,6,(1/4)x)  )}}}{{{drawing(800/3,200,-6,10,-6,6,
circle(2,.5,.24),


graph(800/3,200,-6,10,-6,6,(1/4)x*sqrt(x-2.24)/sqrt(x-2.24))  )}}}

Now we put those chopped-off graphs together, and we have this:

{{{drawing(800/3,200,-6,10,-6,6,
circle(2,.5,.24),


graph(800/3,200,-6,10,-6,6,(1/4)x*sqrt(x-2.24)/sqrt(x-2.24)),
circle(2,2,.2),circle(2,2,.15),circle(2,2,.13),circle(2,2,.1),
circle(2,2,.21),circle(2,2,.19),circle(2,2,.22),circle(2,2,.03),
graph(800/3,200,-6,10,-6,6,((-1/4)x^2+3)*sqrt(2-x)/sqrt(2-x)

)  )}}}

That's the graph of

f(x) = {{{system(   

matrix(2,4,

expr(-1/4)x^2+3,"","", x<=2,
expr(1/4)x, "","",     x>2) ) }}}

Edwin</pre>