How to draw the graph for y= |x| + |x+1| + |x+2| ?

Question

Please list the steps involved

Answer 1

This we have to break into multiple regions

y1 = | x ] means y1 =x > 0
y1 = -x x <0
y2 = | x+1 | means y2 = x+1 x > -1
means y2 = -x-1 x < -1
we need to combine in 3 regions

from the above regions are <=-1 -1 to 0 and >0
for x < -1 y1 = -x, y2 = -x -1 so y1 +y2 = -(2x +1
for x > -1 , x < 0 y1 = -x y2 = x +1 so y1+y2 = 1
for x>0 y1 = x y2 = x+1 y1+y2 = 2x +1

not let y3 = | x+2} y3 = x+2 for x > -2
= -(x-2) for x < -2
now find regons wher y3 is same function and also y1+y2

range < -2, -2 to -1 -1 to 0 >0
for <=-2 y1+y2 = -(2x+1) y3 = - (x+2) y1+y2+y3 = -(3x+3)
for > -2 and <= -1 y1+y2 = -(2x+1) y3 = x+2 y1+y2+y3 = 1-x
for > -1 <= 0 y1+y2 = 1 y3 = x +2 so y1+y2+y3 = x+3
for >0 y1+y2 = 2x +1 y3 = x+2 so sum 3x+3
so the value is found

Answer 2

I don't know if this is the right way of doing it but you could split it up into 4 parts like this:

If x >= 0 then the graph is y = 3x+3
If -1 <= x < 0 then the graph is y = -x+(x+1)+(x+2) = x+3
If -2 <= x < -1 then the graph is y = -x-(x+1)+(x+2) = -x+1
If x < -2 then the graph is y = -x-(x+1)-(x+2) = -3x-3

When drawing the graph, consider each of the 4 regions separately and use the equations above (y=3x+3, y=x+3) to plot the gradient of the line... well that's how I would do it anyway

Answer 3

Draw the graph of
y= I3x+3I

Answer 4

consider the points from negative infinity to -2.Find the value of the given function fo this interval. Similarly consider the intervals(-2,-1) (-1,0) & (0, infinity). find the value of the function for these intervals and plot whatever value u get for all the intervals. the final plot is the required plot.

Answer 5

you will have to separate the diff regions:

Case I:
x<-2
y = -(x) - (x+1) - (x+2)
y = -3x-3

Case II:
-2 y = -(x) - (x+1) + (x+2)
y = -x+1

Case III:
-1 y = -x + (x+1) + (x+2)
y = x+3

Case IV:
x>0
y = x + (x+1) + (x+2)
y = 3x+3

Hence:
-3x-3 , x<-2
-x+1 , -2 y = x+3 , -1 3x+3 , x>0

Answer 6

if you would like a graph, go to www.quickmath.com, click on Plot under Equations, then type in your exact problem, and click plot.

making sure to change the margins if needed.