Question 701627
you are given:

{{{f(x)=2}}} if {{{-infinity<x<=-2}}}

{{{f(x)=(1/2)x+3}}}  if {{{-2<x<=1}}}

{{{f(x)=-(7/8)x+35/8}}}  if {{{1<x<infinity}}}


{{{f(x)=2}}} this is a line parallel to {{{x-axis}}} and has {{{y-intercept}}} at ({{{0}}},{{{2}}})

since you are given that {{{-infinity<x<=-2}}} you can find one more point choosing {{{x}}} less than {{{-2}}} and draw that line all way from certain value of -{{{x}}} to {{{x=-2}}} than stop; that will be at point  ({{{-2}}},{{{2}}}

take second line and choose two values for {{{x}}} so that {{{-2<x<=1}}}

since this line is connected to the first line, use the point  ({{{-2}}},{{{2}}}

and find one more point using {{{x=1}}}

{{{f(x)=(1/2)*1+3}}}

{{{f(x)=(1/2)+3}}}

{{{f(x)=3.5}}}

the second point is ({{{1}}},{{{3.5}}})

plot these points and connect them with a line segment


third part is {{{f(x)=-(7/8)x+35/8}}} or {{{f(x)=-0.875x+4.375}}}  if {{{1<x<infinity}}}

here you start with a point ({{{1}}},{{{3.5}}}) last one you got and find one more point using any {{{x>1}}}

let {{{x=10}}}

{{{f(x)=-0.875*30+4.375}}}

{{{f(x)=-26.25+4.375}}}

{{{f(x)=-21.875}}}

the  point is ({{{30}}},{{{-21.875}}})

plot this point and draw a line from a point ({{{1}}},{{{3.5}}}) and passes through ({{{30}}},{{{-21.875}}})



{{{ graph( 600,600, -15, 15, -15, 15, 2, (1/2)x+3,-0.875x+4.375) }}} 


from this graph where you see all three lines you need to take parts: from a line {{{f(x)=2}}} (red) draw part all way  from  the left to the point ({{{-2}}},{{{2}}}), 

then got to second line {{{f(x)=(1/2)x+3}}} (green) and draw a line segment which connects points ({{{-2}}},{{{2}}}) and ({{{1}}},{{{3.5}}}),

then go to third line {{{f(x)=-(7/8)x+35/8}}} (blue) and draw from the point ({{{1}}},{{{3.5}}}) all way down to the right

that will be your solution, the piecewise function 


{{{drawing(600,600,-30,30,-30,30,

graph(600,600,-30,30,-30,30),
circle(-2,2,.2),circle(1,3.5,.2),line(-30,2,-2,2),line(-2,2,1,3.5),line(30,-21.875,1,3.5)


)  )}}}