Evaluating a Piecewise Function

Piecewise Functions

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

Domain

• The domain of the piecewise function is the union of all of the x-values of the different intervals

• If each interval of each unique function is continous with the interval that precedes it (no gaps), then the domain is defined by the interval from the lowest value of x to the greatest value of x

• If the intervals are not continuous, then the domain is the union of each unique interval.

Domain

​**Copy these Notes on your paper on this slide!!

​Find f(-3).

​Solution: Determine which domain -3 falls within. In this case, it falls within the first piece's domain since -3 is less than -1. Therefore, we use the equation -x+1.

​Plug in -3 in place of the x and simplify.

​f(-3) = - (-3) +1

​ = 3+1

​f(-3)= 4 The answer is 4.

​**Copy these Notes on your paper on this slide!!

​Find f(4).

​Solution: Determine which domain 4 falls within. In this case, it falls within the second piece's domain since 4 is greater than -1. Therefore, we use the equation 2x.

​Plug in 4 in place of the x and simplify.

​f(4) =2 (4)

​ ​f(4)= 8 The answer is 8.

​**Copy in your notes

​Reminder:

​Domain is all possible x-values.

​Range is all possible y-values.

​

Example:

Domain: All Real Numbers

​

​Range: y > 0

​**Copy notes

​Example:

​It has two pieces, each with their own domain, which is listed on graph.

​

​Domain of entire function: x> -4

​

​Range: y> -2

Linear Piecewise Functions

• Includes a combination of lines and line segments

• No specific Shape

• Can be symmetrical, but is not a requirement

• Can touch, but can be disconnected

Continuous vs Discrete

• Continuous graphs have no breaks in them (you could draw them without picking up your pencil)

• Discrete graphs are disconnected (you would have to pick up your pencil to draw them)

Multiple Choice

What is g(7) if:

• -17
• -13 
• 13       
• 17

Multiple Choice

Find f(-2)

• -3
• 6
• 8
• -6

Multiple Choice

Find f(0)

• -3

• 18

• 4

• 0

Multiple Choice

Find h(5) using the equation.

• -25

• 25

• 3

• 7

• undefined

Multiple Choice

Find the value of $$f\left(-8\right)$$ .

• $$21$$  

• $$-8$$  

• $$0$$  

• $$9$$  

Multiple Choice

Graph