How do you write #y = |6 + 2x| + 1 # as a piecewise function?

1 Answer
Nov 30, 2017

Answer:

#y=-(6+2x)+1;x <-3# and
#y=(6+2x)+1;x >-3#

Explanation:

We could say that the absolute equation is shifted 1 units up but in the same x axis. So, We set the expression inside the bar to zero because the absolute means distance from zero but not less than zero. Hence,
#abs (6+2x)=0#
#Or, 6=-2x#
Dividing both sides by #-2#
#6/-2=x#
#:.x=-3#

Hence, the graph will bounce off at #x=-3#
Which divides the graph into two intervals. #(-oo,-3) and (-3,oo)#.

Note that we aren't including #-3# because it will simply turn the expression inside the bar to be zero.
Hence our final piecewise function is.
#y=-(6+2x)+1; if x <-3#
#y=(6+2x)+1; if x>-3#

Note that we are excluding the vertical shift of #1# units because it doesn't afflict the equation.