Piecewise defined 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

Multiple Choice

How many pieces is this Piecewise Function composed of?

• 1

• 2

• 3

• 4

Multiple Choice

Find $$f\left(2\right)$$  

• 3

• 2

Discontinuous

• The function defined for x = 2 is not the same as the function defined at x<2 or x>2
  

Continuous

• The function at x< 0 has the same output value as the function at x > 0

Multiple Choice

Is this piecewise function continuous?

• Yes

• No

Multiple Choice

Where is this piecewise function discontinuous?

• x = -2

• x = 2

• x = -1

• x = 1

Multiple Choice

What is the domain of the graph?

• 1≤ x ≤ 4

• 1 < x < 4

• 1≤ y ≤ 4

• 1 < y < 4

Multiple Choice

What are the domain restrictions for the green piece of this function?

• -2 < x ≤ 1

• -1 < x ≤ 0.5

• x > -2

• x ≤ 1

Evaluating Piecewise Functions

Evaluating an Input to a Piecewise Function

• Look to see where the input value falls into the defined intervals

• Evaluate the input using the corresponding function rule for that interval

Multiple Choice

What is f(6) for the function f(x)=3x-8.

• -8

• 10

• -144

• no answer

Multiple Choice

Given f(x)=2x−10 for which value of x that f(x)=8?

• 5

• 9

• 10

• -12

Multiple Choice

Evaluate $$f\left(-2\right)$$  

• 2

• -8

• 0

• -2

Multiple Choice

What is g(7) if:

• -17

• -13

• 13

• 17