Stitz-Zeager_College_Algebra_e-book

# It would seem natural then that functions should have

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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...
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## 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.

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