Stitz-Zeager_College_Algebra_e-book

It would seem natural then that functions should have

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: of P ? What range t + 15 “makes sense” for this function? What does P (0) represent? What does P (205) represent? 12. Recall that the integers is the set of numbers Z = {. . . , −3, −2, −1, 0, 1, 2, 3, . . .}.8 The greatest integer of x, x , is defined to be the largest integer k with k ≤ x. (a) Find 0.785 , 117 , −2.001 , and π + 6 (b) Discuss with your classmates how x may be described as a piece-wise defined function. HINT: There are infinitely many pieces! (c) Is a + b = a + b always true? What if a or b is an integer? Test some values, make a conjecture, and explain your result. 8 The use of the letter Z for the integers is ostensibly because the German word zahlen means ‘to count.’ 52 Relations and Functions 13. We have through our examples tried to convince you that, in general, f (a + b) = f (a) + f (b). It has been our experience that students refuse to believe us so we’ll try again with a different approach. With the help of your classmates, find a function f for which the following properties are always true. (a) f (0) = f (−1 + 1) = f (−1) + f (1) (b) f (5) = f (2 + 3) = f (2) + f (3) (c) f (−6) = f (0 − 6) = f (0) − f (6) (d) f (a + b) = f (a) + f (b) regardless of what two numbers we give you for a and b. How many...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online