1.3Graphs of Functions part 1

 1.f(-2)=2  f(1)=5  f(3)=27  2. f(-2)=-14  f(1)=1  f(3)=11  3. f(-1)=1  f(0)=-3

 Students will be able to :  *find the domain and ranges of functions and use the vertical line test for functions.  *Determine intervals on which functions are increasing,decreasing,or constant.  * Determine relative maximum and relative minimum values of functions.  Identify even and odd functions.

 The graph of the function f is the collection of ordered pairs (x,f(x)) such that x is in the domain of f.  What is Domain?  Answer: Is the set of all possible values for x  What is Range?  Answer: Is the set of all possible values for y  Example 1 show us how to use the graph od the function to fund the domain and range.

 Find the range of the following figure:  Answer: [-1,1]

 To find the range we can also look at the graph

 Do problems 12 and 13 from book

 What is the vertical line test?  Answer: Is a test use in mathematics to decide whether a given graph represents a function or not.  How does it works?  Answer: basically, in order for a graph to be a function a vertical line can only touch one point each time in the graph. If a vertical line touches two or more points in the graph at a time, then the graph does not represent a function.

Lets see if the graph represents a function or not. Example #1

Does the graph represents a function?

 Its not a function

 Does the graph represents a function?

It’s a function even do it touches two points one of them does not exit.

How do you know when a function is increasing or decreasing ?  Increasing Functions  A function is "increasing" if the y-value increases as the x-value increases, like this:function  It is easy to see that y=f(x) tends to go up as it goes along.

 For a function to increase in the interval when x 1 < x 2 then f(x 1 ) ≤ f(x 2 ) Increasing when x 1 < x 2 then f(x 1 ) < f(x 2 ) Strictly Increasing

 Decreasing Functions  The y-value decreases as the x-value increases: when x 1 < x 2 then f(x 1 ) ≥ f(x 2 ) Decreasing when x 1 f(x 2 ) Strictly Decreasing

 Examples of functions on which intervals does the functions increase, decrease?

 From book page 37  Problems # 7-9  From book page 38  Problems# 19-24

 Today we saw about domain, range, vertical line test and about increasing and deceasing functions.  Tomorrow we are going to continue with the section with relative maxima and minimum and even and odd functions.