Piecewise-defined functions

-- Section 3.3 --

 

Graph the following:
 
There is one function that has 2 different parts.

Solve

Step

Check

Part 1:  yf(x) = 3   

 when x < -2
Horizontal line y = -3

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

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:  yf(x) = x   

when x > -2
Linear function y = f(x) =

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

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:  yf(x) = -x - 2   

 when x < -2
Linear function y = f(x) = -x -

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

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:  yf(x) = 4 - x2   

when  -2 <  x < 2
Quadratic function y = f(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:  yf(x) = x - 2  

when   x > 2
Linear function y = f(x) = x -

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

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