SOLUTION: Equation to be solved is y=|x|+3 and graph results. I understand that the absolute value of |x| is x; therefore the equation would be translated to y = x + 3. My question is is th

Algebra ->  Graphs -> SOLUTION: Equation to be solved is y=|x|+3 and graph results. I understand that the absolute value of |x| is x; therefore the equation would be translated to y = x + 3. My question is is th      Log On


   

Question 156713: Equation to be solved is y=|x|+3 and graph results.
I understand that the absolute value of |x| is x; therefore the equation would be translated to y = x + 3. My question is is this as far as I go with the simiplyfing of this equation or is it more work to be done; and how do I graph.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Well, you're on the right track. If x%3E=0, then abs%28x%29=x. On the other hand, if x%3C0, then abs%28x%29=-x. Consider if x=-2, then abs%28-2%29=-%28-2%29=2

So y=abs%28x%29%2B3 breaks down into y=x%2B3 (if x%3E=0) and y=-x%2B3 (if x%3C0)


To graph y=abs%28x%29%2B3, first graph y=x%2B3 and y=-x%2B3 together on the same coordinate axis:

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B3%2C-x%2B3%29+ Graph of y=x%2B3 (red) and y=-x%2B3 (green)


Since we specified that y=x%2B3 is only true if x%3E=0 and y=-x%2B3 is only true if x%3C0, this means that we only draw the portion that is ABOVE the point of intersection.


So this means that we get:


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+abs%28x%29%2B3%29+ Graph of y=abs%28x%29%2B3