Question 924258
{{{y=abs(2x-3)}}}

find several points, make table,plot points,  and graph the function

{{{x}}}|{{{y}}}

{{{-3}}}|{{{9}}}.....{{{y=abs(2(-3)-3)=abs(-6-3)=abs(-9)=9}}}

{{{-2}}}|{{{7}}}.....{{{y=abs(2(-2)-3)=abs(-4-3)=abs(-7)=7}}}

{{{-1}}}|{{{5}}}.....{{{y=abs(2(-1)-3)=abs(-2-3)=abs(-5)=5}}}

{{{0}}}|{{{3}}}.....{{{y=abs(2(0)-3)=abs(0-3)=abs(-3)=3}}}

{{{1}}}|{{{1}}}.....{{{y=abs(2(1)-3)=abs(2-3)=abs(-1)=1}}}

{{{2}}}|{{{1}}}.....{{{y=abs(2(2)-3)=abs(4-3)=abs(1)=1}}}

{{{3}}}|{{{3}}}.....{{{y=abs(2(3)-3)=abs(6-3)=abs(3)=3}}}

{{{5}}}|{{{7}}}.....{{{y=abs(2(5)-3)=abs(10-3)=abs(7)=7}}}

plot these points and graph:

{{{drawing( 600, 600, -10,10, -10, 10,circle(5,7,.12),locate(5,7,p(5,7)),circle(3,3,.12),locate(3,3,p(3,3)),circle(2,1,.12),locate(2,1,p(2,1)),circle(1,1,.12),locate(1,1,p(1,1)),circle(0,3,.12),locate(0,3,p(0,3)),circle(-1,5,.12),locate(-1,5,p(-1,5)),circle(-2,7,.12),locate(-2,7,p(-2,7)),circle(-3,9,.12),locate(-3,9,p(-3,9)), graph( 600, 600, -10,10, -10, 10, abs(2x-3))) }}} 


domain:

{{{R}}}  (all real numbers)

range:

{ {{{y}}} element {{{R}}} : {{{y>=0}}} }  (all non-negative real numbers)


2.

{{{x+3=abs(y)}}}=> {{{x+3 = sqrt(y^2)}}}=> {{{x+3 = y}}} or {{{x+3 = -y}}}

{{{x+3 = y}}} 
{{{x+3 = -y}}}=>{{{-x-3 = y}}} 

 

{{{x}}}|{{{y}}}

{{{-3}}}|{{{0}}}.....{{{abs(y)=x+3=-3+3=0}}}

{{{-2}}}|{{{1}}}.....{{{abs(y)=x+3=-2+3=1}}}=>{{{y=1}}} or {{{y=-1}}}
{{{-2}}}|{{{-1}}}

{{{-1}}}|{{{2}}}.....{{{abs(y)=x+3=-1+3=2}}}=>{{{y=2}}} or {{{y=-2}}}
{{{-1}}}|{{{-2}}}

{{{0}}}|{{{3}}}.....{{{abs(y)=x+3=0+3=3}}}=>{{{y=3}}} or {{{y=-3}}}
{{{0}}}|{{{-3}}}

{{{1}}}|{{{4}}}.....{{{abs(y)=x+3=1+3=4}}}=>{{{y=4}}} or {{{y=-4}}}
{{{1}}}|{{{-4}}}

{{{5}}}|{{{8}}}.....{{{abs(y)=x+3=5+3=8}}}=>{{{y=8}}} or {{{y=-8}}}
{{{5}}}|{{{-8}}}

{{{drawing( 600, 600, -10,10, -10, 10,blue(line(-3,0,5,-8)),blue(line(-3,0,5,8)),circle(-3,0,.12),locate(-3,0,p(-3,0)),circle(-2,1,.12),locate(-2,1,p(-2,1)),circle(-2,-1,.12),locate(-2,-1,p(-2,-1)),circle(-1,2,.12),locate(-1,2,p(-1,2)),circle(-1,-2,.12),locate(-1,-2,p(-1,-2)),circle(0,3,.12),locate(0,3,p(0,3)),circle(0,-3,.12),locate(0,-3,p(0,-3)),circle(1,4,.12),locate(1,4,p(1,4)),circle(1,-4,.12),locate(1,-4,p(1,-4)), graph( 600, 600, -10,10, -10, 10, 0)) }}}


domain:
{{{R^2}}}
range:
unable to determine range 
{{{Re(x)>-3}}}