SOLUTION: describe the transformation of g(x)=|x-2|+2 Is it possible that the answer is "impossible geometric transformation"? The absolute value confuses me.

Algebra ->  Rational-functions -> SOLUTION: describe the transformation of g(x)=|x-2|+2 Is it possible that the answer is "impossible geometric transformation"? The absolute value confuses me.       Log On


   

Question 882998: describe the transformation of g(x)=|x-2|+2
Is it possible that the answer is "impossible geometric transformation"? The absolute value confuses me.
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
x-2 can be 0 or positive or negative. A change occurs at x=2.

The case, x-2%3C0 means g%28x%29=-%28x-2%29%2B2=-x%2B2%2B2=-x%2B4;
Think carefully about the meaning of absolute value and maybe draw and label a numberline to see that.

The case x-2=0 means x=2 and then g%28x%29=2.

The case, x-2%3E0 means g%28x%29=x-2%2B2=x%2B0=x.

To understand this as a transformation, you would have started with highlight_green%28f%28x%29=abs%28x%29%29; and then the x-2 means shifting two units to the right, and then the highlight%28y=g%28x%29=abs%28x-2%29%2B2%29 means shifting two units upward.

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

Instead of this "simpler" function:
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cabs%28x%29%29