Читать книгу Algebra I All-in-One For Dummies - Mary Jane Sterling, Mary Sterling Jane - Страница 47

You may have never used the greatest integer function before, but you’ve certainly been its victim. Utility and phone companies and sales tax schedules use this function to get rid of fractional values. Do the fractions get dropped off? Why, of course not. The amount is rounded up to the next greatest integer.

The greatest integer function takes any real number that isn’t an integer and changes it to the greatest integer it exceeds. If the number is already an integer, then it stays the same.

The symbol for the greatest integer function is a set of brackets, . You put your number in question in the brackets, evaluate it, and out pops the answer.

Q. Find the absolute value:

A. . The distance from –4 to 0 is 4 units.

Q. Evaluate:

A. . You perform the operation inside the absolute value bars before evaluating.

Q. Evaluate 3!

A.

Q. Evaluate 6!

A.

Q. Evaluate:

A. . The number 6 is the biggest integer that is not larger than .

Q. Evaluate:

A. . Just picture the number line. The number –3.87 is to the right of –4, so the greatest integer not exceeding –3.87 is –4. In fact, a good way to compute the greatest integer is to picture the value’s position on the number line and slide back to the closest integer to the left — if the value isn’t already an integer.

15 Determine which is greater: or 3!

16 Determine which is greater: or .

17 Determine which is greater: 5! or .

18 Determine which is greater: or .