2.5 Piecewise Functions

Solving System of Equations:

Graph & Find intersection points

Solutions:

(x, y): point

x={x₁, x₂,..}: x-values of intersection points

No intersection: No solution

Answers could be:

 $\left(-1,\ 1\right)\ \&\ \left(2,\ 4\right)$  

 $x=\left\{-1,\ 2\right\}$  

Solving Systems of Inequalities

Graph in Desmos & See where the shaded regions overlap

Solutions: ordered pairs in shaded region

No overlap in shading: no solution

BE CAREFUL! points on dotted lines are NOT apart of solutions

 $\left(0,\ 0.5\right)$  is a solution

 $\left(1,\ 1\right)$  is a solution

 $\left(-1,\ 1\right)$  is not a solution

 $\left(2,\ -1\right)$  is not a solution

A function defined by 2 or more functions over a specified domain.

We can either:

Evaluate piecewise functions

Graph piecewise functions

Find key features of piecewise functions

Evaluating PW Functions is just like evaluating functions!

Ex. Find  $f\left(2\right)$  

Find y when x=2

Since $2\ge0$ 

  We evaluate  $f\left(2\right)=2-1$  

 $f\left(2\right)=1$  

Find

 $-2<0$  so  $f\left(-2\right)=\left(-2\right)^2+1$  

 $f\left(-2\right)=5$