SOLUTION: I come to this site for assistance on step by step instruction to fully understand how to work out problems, as it has been my life saver. Unfortunately my textbook is not very th

Algebra ->  Absolute-value -> SOLUTION: I come to this site for assistance on step by step instruction to fully understand how to work out problems, as it has been my life saver. Unfortunately my textbook is not very th      Log On


   

Question 951300: I come to this site for assistance on step by step instruction to fully understand how to work out problems, as it has been my life saver. Unfortunately my textbook is not very thorough with explanations. The instruction is: Graph each absolute value function and state its domain and range. I greatly appreciate the help and terribly need step by step instruction so I may complete remaining homework. Thank you. The problem is: g(x)=x+2.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You said, "... absolute value...". Do you mean for the example, g%28x%29=abs%28x%2B2%29?

Best approach is, find an alternative textbook!

Use two conditions for your function. x+2 is non-negative and x+2 is negative.

NON-NEGATIVE
x%3E=-2----necessary for this condition;
g%28x%29=x%2B2
This branch starts at -2, and NOTHING to the left. Includes point (-2,0), and also (0,2) as you would expect from linear equation in this interval.

NEGATIVE
x%3C-2-----necessary for this condition;
g%28x%29=-%28x%2B2%29
g%28x%29=-x-2
No vertical axis intercept here because x=0 NOT in this interval.


Summary of the two parts:
-----------------------------------
g%28x%29=x%2B2 , x%3E=-2
-----------------------------------
g%28x%29=-x-2, x%3C-2
-----------------------------------

graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cabs%28x%2B2%29%29

REMIND: Absolute Value is never negative.