1-3 Functions and their graphs part 2

 Students will be able to:  * Determine relative maximum and relative minimum values of functions  * Identify and graph step functions and other piece-wise defined functions.  * Identify even and odd functions

 What is a relative Maximum?  Answer: a relative maximum is the highest point in the graph.  WE SAY THAT A FUNCTION f(x) has a relative maximum value at x = a, if f(a) is greater than any value immediately preceding or following.  We call it a "relative" maximum because other values of the function may in fact be greater.

 What is Relative Minimum  Answer: a relative minimum is the lowest point in the graph.  We say that a function f(x) has a relative minimum value at x = b, if f(b) is less than any value immediately preceding or following.

Relative Maximum Relative Minimum

Label the relative maximum and minimum of the following graph Relative Maximum Relative Minimum

 Polynomials of degree greater than 2: Polynomials of degree greater than 2 can have more than one max or min value. The largest possible number of minimum or maximum points is one less than the degree of the polynomial. The following examples illustrate several possibilities. In each case, the accompanying graph is shown under the discussion.

 What is a piecewise function?  Answer: is a function which is defined by multiple sub functions, each sub function applying to a certain interval of the main function's domain (a subdomain).function

 What is an Even function?  Answer: Is a function whose graph is symmetric about the y-axis.  What is an Odd function?  Answer: Is a function whose graph is symmetric with respect to the origin.

Symmetric to y-axis Even function Symmetric to origin Odd Function

Symmetric about the x-axis NO a function(neither)

 Determine if the graph belong to an even, odd or neither function  A. Even function

B. C. Odd function Neither

 Lets do problems 65 ad 67 from page 38.

Problems 35-38, 55,56,66,68 from book page 38

 Today we saw about relative maxima, relative minima, piece wise function and how to determine even and odd functions. Tomorrow we are going to continue with section 5 from book.