Question 122658
In order to graph {{{y=abs(x)+3}}} we need to plot some points. In order to find some points, we need to plug in some x values


{{{y=abs(x)+3}}} Start with the given equation



{{{y=abs(-2)+3}}} Plug in {{{x=-2}}}



{{{y=2+3}}} Evaluate the absolute value of -2 to get 2



{{{y=5}}} Add



So our first point is (-2,5)



Let's plot the 1st point (-2,5)

{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,5,0.05),
  circle(-2,5,0.08)
  )}}}



Let's find the 2nd point


{{{y=abs(x)+3}}} Start with the given equation



{{{y=abs(-1)+3}}} Plug in {{{x=-1}}}



{{{y=1+3}}} Evaluate the absolute value of -1 to get 1



{{{y=4}}} Add


So our 2nd point is (-1,4)



Plot the 2nd point (-1,4)

{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,5,0.05),
  circle(-2,5,0.08),circle(-1,4,0.05),
  circle(-1,4,0.08)
  )}}}




Let's find the 3rd point


{{{y=abs(x)+3}}} Start with the given equation



{{{y=abs(0)+3}}} Plug in {{{x=0}}}



{{{y=0+3}}} Evaluate the absolute value of 0 to get 0



{{{y=3}}} Add


So our 3rd point is (0,3)




Plot the 3rd point (0,3)

{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,5,0.05),
  circle(-2,5,0.08),circle(-1,4,0.05),
  circle(-1,4,0.08),circle(0,3,0.05),
  circle(0,3,0.08)
  )}}}





Let's find the 4th point


{{{y=abs(x)+3}}} Start with the given equation



{{{y=abs(1)+3}}} Plug in {{{x=1}}}



{{{y=1+3}}} Evaluate the absolute value of 1 to get 1



{{{y=4}}} Add


So our 4th point is (1,4)




Plot the 4th point (1,4)

{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,5,0.05),
  circle(-2,5,0.08),circle(-1,4,0.05),
  circle(-1,4,0.08),circle(0,3,0.05),
  circle(0,3,0.08),circle(1,4,0.05),
  circle(1,4,0.08)
  )}}}





Let's find the 5th point


{{{y=abs(x)+3}}} Start with the given equation



{{{y=abs(2)+3}}} Plug in {{{x=2}}}



{{{y=2+3}}} Evaluate the absolute value of 2 to get 2



{{{y=5}}} Add


So our 2nd point is (2,5)




Plot the 5th point (2,5)

{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,5,0.05),
  circle(-2,5,0.08),circle(-1,4,0.05),
  circle(-1,4,0.08),circle(0,3,0.05),
  circle(0,3,0.08),circle(1,4,0.05),
  circle(1,4,0.08),circle(2,5,0.05),
  circle(2,5,0.08)
  )}}}



Now draw a line through all of the points to graph {{{y=abs(x)+3}}}



{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),
  graph( 700, 700, -10, 10, -10, 10,abs(x)+3),
  circle(-2,5,0.05),
  circle(-2,5,0.08),circle(-1,4,0.05),
  circle(-1,4,0.08),circle(0,3,0.05),
  circle(0,3,0.08),circle(1,4,0.05),
  circle(1,4,0.08),circle(2,5,0.05),
  circle(2,5,0.08)
  )}}}



Answer:

So the graph of {{{y=abs(x)+3}}} is


{{{graph( 700, 700, -10, 10, -10, 10,abs(x)+3)}}}