CLASS OPENER: You have 5 minutes to come up with the largest prime number you possible can.

HOMEWORK REVIEW Pg. 11 – 13 #10, 55, 72

A FUNCTION: A function f from set A to set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain of the function f, and the set B contains the range of the function.

CHARACTERISTICS OF A FUNCTION 1.Each element of A much be matched with an element of B 2.Some elements of B may not be matched with any element of A 3.Two or more elements of A may be matched with the same element of B 4.An element of A cannot be matched with two different elements of B

EXAMPLE:

REVIEW OF FUNCTION NOTATION f(x) = range x = domain

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PIECEWISE FUNCTION A piecewise –defined function is a function that is defined by two or more equations over a specified domain. The absolute value function given by f(x) = x can be written as a piecewise – defined function.

EXAMPLE

EXAMPLE: Evaluate the function at each specified value of the independent variable and simplify a)f(-1)b) f(0)c) f(2)

IMPLIED DOMAIN

RADICAL FUNCTIONS Radical functions arise from the use of rational exponents. The most common radical function is the square root function.

CLASS OPENER: A rectangular package to be sent by the U.S. Postal Service can have a maximum combined length and girth(perimeter of cross section) of 108 inches. a)Write the volume V of the package as a function of x. What is the domain of the function? b)Use a graphing utility to graph the function. Make sure to have the appropriate window. c)What dimensions will maximize the volume of the package?

EXAMPLE:

PUT TECHNOLOGY TO WORK

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REAL WORLD CONNECTIONS

PHYSICS CONNECTION

CALCULUS CONNECTION

EVALUATING WITH DIFFERENCE QUOTIENT

FIND THE DIFFERENCE QUOTIENT

ASSIGNMENT Pg. 11 – 15 Exs. 12 – 32 even, 39 – 46, 52 – 62 even, 68 – 74 even, 79 – 82, 85 – 87, 91 – 102, 113 – 116