How do you write #y = |6 + 2x| + 1 # as a piecewise function?
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,
Dividing both sides by
Hence, the graph will bounce off at
Which divides the graph into two intervals.
Note that we aren't including
Hence our final piecewise function is.
Note that we are excluding the vertical shift of