2.5 Piecewise Functions

2.5 Piecewise Functions

Objective: Evaluate and identify key features of piecewise functions

But First, Review of Systems!!

• Solving System of Equations:

• Graph & Find intersection points

• Solutions:

• (x, y): point

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

• No intersection: No solution

Find where f(x) = g(x)

• Answers could be:

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

•  $x=\left\{-1,\ 2\right\}$  

Review of Systems

• 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

Which of the following points are 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

• 
  

Piecewise Functions

• 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 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  $f\left(2\right)=2-1$  

•  $f\left(2\right)=1$  

Another Example

• Find

   $f\left(-2\right)$ 

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

•  $f\left(-2\right)=5$  

Multiple Choice

Find

 $f\left(-2\right)$  

• -3

• -2

• -1

• 0

Fill in the Blanks

Find  $f\left(0\right)$  

Multiple Choice

Evaluate $f\left(-2\right)$  

• 2

• -8

• 0

• -2

Fill in the Blanks

 $f\left(3\right)$  

Find

Multiple Choice

Find $f\left(2\right)$  

• 3

• 2

Fill in the Blanks

Find $f\left(1.56\right)$