Today in Pre-Calculus Go over homework Notes: Determining if a function is bounded below, bounded above or unbounded - need a calculator Homework

incr: (- ∞, ∞) decr: (- ∞, 0 ) incr: (0, ∞) decr: (- ∞, 0 ) incr: (0, ∞) decr: ( 3, 5 ) incr: (-∞, 3 ) constant: ( 5, ∞) decr: ( 3, ∞) incr: (-∞, 0 ) constant: (0, 3) decr: (- 1, 1) incr: (- ∞, -1 ), ( 1, ∞) decr: (- ∞, ∞) incr: (- ∞, 0) decr: (0, ∞) decr: (- ∞, -4) incr: ( 4, ∞) decr: (2,∞) incr: (-∞,-2) constant(-2,2) Inc(0,3) decr: (- ∞, 0) cons: (3, ∞) decr: ( - ∞, 7)υ (7, ∞)

Functions Bounded Below Definition: A function f is bounded below if there is some number b that is less than or equal to every number in the range of f. Answers is in terms of y-values Any such number b is called a lower bound of f. In this graph b=-2

Functions Bounded Above A function f is bounded above if there is some number B that is greater than or equal to every number in the range of f. Any such number B is called an upper bound of f. In this graph B = 3

Bounded A function f is bounded if it is bounded from both above and below. In this graph b = -1 and B = 1.

Unbounded A function f is unbounded if it is neither bounded from above and below. As separate pieces (or branches), the lower piece is bounded above and the upper piece is bounded below, however as a whole the function f is unbounded.

Example 1 Bounded below b = 3 Prove Algebraically: x2≥0 2x2≥0

Example 2 Bounded b = -1 B = 1

Example 3 Bounded above B = 5

Example 4 unbounded

Homework Wkst.