How do you write x=-|y+1|+4 as piecewise functions?

Jan 14, 2018

$f \left(y\right) = \left\{\begin{matrix}y > - 1 \text{ & " -x+3 \\ y<=-1 " & } x - 5\end{matrix}\right.$

Explanation:

Since the equation in rotated due to have x and y switched, we will use y values as the constraints.

Find the vertex through knowledge of function transformations$\left(4 , - 1\right)$.
Then, since the equation was rotated, find how far up and down the y-intercepts are:
$\left(0 , 3\right) \left(0 , - 5\right)$

Finally, write the piecewise function using the vertex to find the constraints and the y-intercepts to find the function that each section of the original will become.