The Greatest Integer Function (3.13.1)

Question 1

• The greatest integer function looks for the greatest integer that is less than or equal to x in the notation [x].

Answer 1

• The greatest integer function looks for the greatest integer that is less than or equal to x in the notation [x].

Question 2

• The graph of this function is sometimes referred to as a “step-function” because of its appearance.

Answer 2

• The graph of this function is sometimes referred to as a “step-function” because of its appearance.

Question 3

Here are some examples that satisfy the
greatest integer function.

Note: When the greatest integer function is evaluated with a negative non-integer input value, the result is an integer that is further from zero than the input value.

Visualize the positions on a number line to help you make your choice.

Because the fraction values of x result in integer values for y, the graph looks like stair steps of short horizontal lines.

For example, for every x-value between 1.0 and 2.0, the y-values equal 1.

Likewise for every x-value between –2 and –1, the y-values equal –2. You can see these in the graph in this example.

Answer 3

Here are some examples that satisfy the
greatest integer function.

Note: When the greatest integer function is evaluated with a negative non-integer input value, the result is an integer that is further from zero than the input value.

Visualize the positions on a number line to help you make your choice.

Because the fraction values of x result in integer values for y, the graph looks like stair steps of short horizontal lines.

For example, for every x-value between 1.0 and 2.0, the y-values equal 1.

Likewise for every x-value between –2 and –1, the y-values equal –2. You can see these in the graph in this example.