Solution for Problem 3.3.2

Graph the following:

There is one function that has 3 different parts.

Solve

Step

Check

Part 1:  y =  h(x) = -x   

 when x < 0
Linear function
y = h(x) = -x

The open circle denotes that 0 is not
 included since  x < 0

Click here for Lines Tutorial.

 h(-5) =  -(-5)  = 5
  since -5 < 0

h(-3) =  -(-3) = 3
  since -3 < 0

h(-1) = -(-1) =1
since -1 < 0
               

Part 2:  y =  h(x) = x2 

when  0 <  x < 2
Quadratic function 
y = h(x) = x2   

The closed circle denotes that 0 and 2 is  included since  0 <  x < 2

Click here for Quadratic Tutorial.

 

  h(0) = 02  = 0
  since 0 <  0 < 2

h(1) = 12  = 1
  since 0 <  1 < 2

h(2) = 22  = 4 
  since 0 <  2 < 2

Part 3:  y =  h(x) = 4  

when   x > 2
Linear function y = h(x) = 4 

The open circle denotes that 2 is not
 included since  x > -2

Click here for Lines Tutorial.

 h(3) = 4
  since 3 > 2

h(4) =  4 
  since 4 > 2

h(5) = 4 
since 5 > 2

Put both parts together...

It is beautiful!

Notice the open circles and closed circles overlap.