# Week 13 – Pre Calculus 11

This week in Pre-Calculus 11 we were introduced to our next unit of Absolute Value and Reciprocal Functions. In this unit, we will be focusing on finding if an absolute value function $y=|f(x)|$ can be expressed as either y=f(x) or y=-f(x) for subset domain. Also graphing reciprocal functions $y= 1/f(x)$. All these skills will eventually lead to giving us the ability to operate and analyzing rational functions.

So far in this unit, I have had only one thing that is troubling me and that is writing the equations on piecewise notation. I understand how to write the equation by the thing that is confusing for me is writing what is greater than or less than or equal to.

Down below you will see an example of Piecewise notation:

Graph y=|-2x+5| and write in piecewise notation

To find how this graph looks in piecewise notation we must first find the reciprocal of the equation. To find that I must multiply everything by -1.

f(x)= {-2x+5                                                                                                                                                                                                                                                     { 2x-5

Now we must find if it is greater than or less than or equal to a number. To find this we need to look at the graph, first out x intercept or critical point is on 2.5 so our first so our first value will be x>=2.5. And for the bottom one we will get x < 2.5

So our final piecewise notaion will look something like this:

f(x)= {-2x+5 ,  x>=2.5                                                                                                                                                                                                                                    { 2x-5 , x < 2.5