Question

f(x)=|(x+2)^3-1|
what will be the two functions?

Answer 1

First you must find where the function inside the absolute value is zero,
\[(x+2)^3-1=0\Rightarrow x+2=1\Rightarrow x=-1\]Then, you need to find the sign of the function,
\[x<-1\Rightarrow (x+2)^3-1<0\\
x>-1\Rightarrow (x+2)^3-1>0\] So, the functions will be,
\[x<-1\Rightarrow-( (x+2)^3-1)\\
x>-1\Rightarrow (x+2)^3-1\]

Answer 2

Where did those inequalities come from?

Answer 3

so if I graph x>1, does that mean the function will be
*reflected in the x-axis
*shift 3 units to the left
*1 unit up?

Answer 4

Yes, it should be that way. I attach a plot of the figure near x=-1.

Answer 5

wolfram alpha....
so the negative is for the whole function, and I need to multiply the negative to each term?