Question 157686
f(x) = { x - 4, {{{ x <= 2 }}} }
.........{ 2x + 3, {{{ 2 < x <= 14 }}} }
.........{ 36, {{{ x > 14 }}} }

f is defined using three formulas for linear function, so graph all three of them

 graph first this linear function: {{{f(x) =  x - 4}}}, for {{{ x <= 2 }}} ...........since we have a restriction {{{ x <= 2 }}}, erase the part {{{x>=2}}}
the domain is ( {{{ - infinity  }}},{{{ 2 }}})


then graph this linear function: {{{f(x) =  2x + 3}}}, for {{{ 2 < x <= 14 }}} ...........since we have a restriction {{{ 2<=x }}}, erase the part from {{{-infinity}}} to {{{2}}} and the part where {{{x >= 14}}}
this graph will be a line segment from {{{x=2}}} to {{{x=14}}}
the domain is ( {{{ 2 }}},{{{ 14 }}}) 


then graph this linear function: {{{f(x) = 36}}}, for {{{ x > 14 }}}
this is constant function, so it is define for [{{{ 14 < x <infinity}}})

the domain is [{{{ 14 < x <infinity}}})