Graph y=x-|x|: Is There a Solution?

[mikebc]

confused ... y=x-|x|

The problem is to graph this equation y=x-|x|.



From what I understand of absolute values, this x would be positive. If it is positive then y=0 and there would be no points to graph. Is there something that I am missing? The question is worth 4 points, so I can't see the answer just being 0. Thanks for any suggestions.

 

[D H]

What happens when x is negative?

 

[dranseth]

What I was taught to do when dealing with absolute value, is to rewrite the equation so that the absolute value is isolated, then find the 2 equations.

so you'll have:
x=x-y
y=o

and also:
x=-x+y
2x=y

 

[mikebc]

The absolute value of -x would be x. But I remember with inequalities there are 2 possible answers with absolute value (-,+). From what you are explaining it sounds like that is what you are saying to do, use both possible values. Then I would graph by beginning with y at 0 and continue by substituting values into 2x=y? That seems to make sense to me. Thank you both for your help!

 

[K.J.Healey]

Also just try plugging in some numbers:
For 2 -> Y = 2 - |2| = 0
For -2 - > Y = -2 -|-2| = -2 -2 = -4
see?
So for negatives you have Y = 2X, X<0

 

[symbolipoint]

Solve or graph y = x - |x|.

If x>0, then y = x - x, meaning y=0.

If x<0, then y = x - (-x) [ notice those are parentheses, not absolute value notation symbols ], meaning y = x + x = 2x.

 

[HallsofIvy]

The problem is to graph this equation y=x-|x|.



From what I understand of absolute values, this x would be positive.

Surely you didn't mean to say that! x itself can be any number. |x| is always positive (or 0- don't forget that!

What I was taught to do when dealing with absolute value, is to rewrite the equation so that the absolute value is isolated, then find the 2 equations.

so you'll have:
x=x-y
y=o

Why did you switch to x=? If x\ge 0 y= x- x= 0. The graph is just the x-axis from x= 0 to the right.

and also:
x=-x+y
2x=y

If x< 0, don't forget that. Then y= x- (-x)= 2x.

The absolute value of -x would be x.

No, no, no! |-x|= |x| which may be eigther x or -x depending upon what x is.

But I remember with inequalities there are 2 possible answers with absolute value (-,+). From what you are explaining it sounds like that is what you are saying to do, use both possible values. Then I would graph by beginning with y at 0 and continue by substituting values into 2x=y? That seems to make sense to me. Thank you both for your help!

Draw the graph of y= 2x, to the left of x= 0. To the right, the graph is just y= 0, the x-axis.

 

[dranseth]

I rearranged the formula to isolate the absolute value.

 

[mikebc]

Wow, you guys couldn't have made it any more clear for me. Thanks a lot!