Drawing Functions & Back Again

Take the following graph

In order to recreate (one possible) function we need to do the following:

1. Determine the end-behavior, and decide if it’s a reflection or not (this one is a reflection of a ^2!)
2. Determine its stretch/squash
   • count the squares, if its over more than 1 then add that many as the denominator (the above would be 1/2) and you got the coefficient!
   • Otherwise if its taller more than 1 before it crosses a point add that many and add that as the coefficient!
     • 
       • This would be 2!
       • Think of it like when you find the slope, by going $\frac{rise}{run}$
3. Next add the adjustments to the vertex as appropriate! inside the parathesis for horizontal movement and outside for vertical movement