Piecewisedefined functions 
 Section 3.3  

Graph the following: 
There is one function that has 2 different parts.  
Solve 
Step 
Check 
Part 1: y = f(x) = 3 
when x < 2  
Horizontal line y =
3
The open circle denotes that 2 is not Click here for Lines Tutorial. 
f(10) = 3 since 10 <
2
f(6) = 3 since 6 < 2 f(1.9) = 3 since 1.9 < 2 f(2) = 2 since 2 > 2 

Part 2: y = f(x) = x 
when x > 2  
Linear function y =
f(x) = x
The closed circle denotes that 2 is not Click here for Lines Tutorial.

f(2) = 2 since 2 >
2
f(0) = 0 since 0 > 2 f(2) = 2 since 2 > 2 f(4) = 4 since 4 > 2 

Put both parts together... 

It is beautiful!  
Graph the following: 
[Solution] 

Graph the following: 
There is one function that has 3 different parts.  
Solve 
Step 
Check 
Part 1: y = f(x) = x  2 
when x < 2  
Linear function y =
f(x) =
x  2
The open circle denotes that 2 is not included Click here for Lines Tutorial. 
f(5) = (5) 
2 = 3 since 5 <
2
f(4) = (4)  2 = 2 since 4 < 2 f(3) = (3)  2 = 1since 1.9 < 2 

Part 2: y = f(x) = 4  x^{2} 
when 2 < x < 2  
Quadratic function y =
f(x) = x
The closed circle denotes that 2 and 2 is included since 2 < x < 2 Click here for Quadratic Tutorial.

f(2) = 4  (2)^{2} =
4  4 = 0
since 2 < 2 <
2 f(1) = 4  (1)^{2} = 4  1 = 3 since 2 < 1 < 2 f(0) = 4  (0)^{2} = 4  0 = 4 since 2 < 0 < 2 f(1) = 4  (1)^{2} = 4  1 = 3 since 2 < 1 < 2 f(2) = 4  (2)^{2} = 4  4 = 0 since 2 < 2 < 2 

Part 3: y = f(x) = x  2 
when x > 2  
Linear function y =
f(x) = x
 2
The open circle denotes that 2 is not Click here for Lines Tutorial. 
f(3) = 3  2 = 1 since
3 > 2 f(4) = 4  2 = 2 since 4 > 2 f(5) = 5  2 = 3since 5 > 2 

Put both parts together... 

It is beautiful!
Notice the open circles and closed circles overlap. 

Graph the following: 
[Solution] 

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada