A# ___________

6, x 2

f (x) x, 2 x 2

3, x 2

− ≤ −

= − < ≤ >

Piecewise and Step Functions Worksheet

1) Evaluate

a) � �5.7 =

b) 2 5 =� �� �� �

c) � �3π =

d) � �6.1− =

e) � �0.2 =

f) � �5 9.1− =

2) Sketch the graph of

� �f (x) x= from 4 x 4− ≤ <

3) Sketch the graph of

� �f (x) 3 x= from 2 x 2− ≤ <

4) Sketch the graph of

� �f (x) 2 x= − from 0 x 5≤ <

Sketch the following piecewise functions. For problem 7 only, state the range and extreme value(s).

5) 6) 7)

x 3, x 1f (x)

2x, x 1

+ <=

≥

2x , x 2

f (x)2x, x 2

<=

≥

2

2

2x , x 0

f (x) 2x 1, 0 x 1

4, x 1

− ≤

= + < < ≥

Sketch the following piecewise functions.

8) 9)

10)

11) 3

4, 5

( ) , 2 2

3, 3

x

f x x x

x x

< −

= − ≤ ≤

+ >

2

x , x 0f (x)

x 3, x 0

≥=

− − <

( )2

x 4 , x 2f (x)

x 1 , x 2

+ < −=

+ ≥ −