Greatest Integer/Absolute Value Functions

1
Greatest Integer/Absolute Value Functions

• Students will be able to find greatest integers
  and absolute values and graph the both functions.

2
Greatest Integer

• Another special function that we will be studying
  is the greatest integer function. The greatest
  integer function of a real number x, represented
  by x, is the greatest integer that is less than
  or equal to x.
• For example
• 4.25 4 6 6 5.99 5 -2.3
  -3

3

• Determine whether each statement below is true or
  false for all real numbers x and y.
• x y x y
• if x 4.2 and y 3.1, then x y 7.3
• 4.2 3.1 7.3
• 4 3 7 Is this
  correct?
• if x 4.7 and y 3.9, then x y 8.6
• 4.7 3.9 8.6
• 4 3 8 Is this
  correct?

4
Graph

• The greatest integer function is sometimes called
  a step function, because of the shape of its
  graph.
• Graph y x

5
Graph

• What happens when we change the function? First
  multiply the function by 2.
• Graph y 2x
• On calculator
• y 2int(X)

6
Graph

• What happens when we change the function? Next
  multiply the independent variable by 2.
• Graph y 2x
• On calculator
• y int(2X)

7
Absolute Value

• All integers are composed of two parts the size
  and the direction. For example, 5 is five units
  in the positive direction 5 is five units in
  the negative direction.
• The absolute value written like this of
  a number gives the size of the number without the
  direction. For example, 5 and 5.
  The answer is always positive.

8
Absolute Value

• Graphing the absolute value function.
• Graph

x y
-4
-2
0
2
4
4 2 0 2 4