Section 3.5C: Graphs of Functions

• Sketch Piecewise-Defined Functions:

Ex: f (x) 2x 3 if x 0x 2 if 0 x 2

1 if x 2

• Is the function even, odd, or neither?

Ex: f (x) 3x 4 2x 2 5

• Is the function even, odd, or neither?

Ex: f (x) 2x 5 7x 3 4x

• Is the function even, odd, or neither?

Ex: f (x) 2x 3 7x 2 4x 6

Summary:

• If f(x) = f(-x), then it is “even.”

• If -f(x) = f(-x), then it is “odd.”

Even, odd, or neither??

Ex: f (x) 3x 3 x

Ex: f (x) 3x 2 x

Ex: f (x) 3x 2 1

• Sketch the Greatest Integer Function:

Define Integer:

-4 -3 -2 -1 0 1 2 3 4

The “Greatest Integer Function” will turn every number into an integer!!

Ex: 2.7

Ex: 1.1

Ex: 1.1

Ex:

• Sketch the Greatest Integer Function:

f (x) x

x y

Sketch the Greatest Integer Function w/ Transformations:

f (x) x

f (x) x 3

Transformation:

Sketch the Greatest Integer Function w/ Transformations:

f (x) x

Transformation:

f (x) 2x

Sketch the Greatest Integer Function w/ Transformations:

f (x) x

Transformation:

f (x) 2 x

Sketch the Greatest Integer Function w/ Transformations:

f (x) x

Transformation:

f (x) x

Sketch the Greatest Integer Function w/ Transformations:

f (x) x

Transformation:

f (x) x