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

1 Answer
Nov 30, 2017

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.