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

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,
$\left\mid 6 + 2 x \right\mid = 0$
$O r , 6 = - 2 x$
Dividing both sides by $- 2$
$\frac{6}{-} 2 = x$
$\therefore x = - 3$

Hence, the graph will bounce off at $x = - 3$
Which divides the graph into two intervals. $\left(- \infty , - 3\right) \mathmr{and} \left(- 3 , \infty\right)$.

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.