Blog 4: Domain and Range - Bianca

Bianca Flores
4/18/15
           
                                                                    Be the Professor
   
Lecture Topic: Domain & Range

Introduction: 

                       Hello, my name is Professor Flores and today I am going to teach you how to find the Domain & Range of a function on a graph.

What are Domain & Range?:

• Domain: set of all input values (x-axis values on a graph) of a function
• Range: set of all output values (y-axis values on a graph) of a function

What is a function?:

• a relationship involving one or more variables

ex.: y=mx+b (linear function)

How do we find Domain & Range on a graph?

equation of graph: y=x+5

Domain: To find the domain of a function, on a graph you can visually see the extent of the line of the equation and therefore see how far the line stretches across the x-axis.

•          ex.: In the graph above, you can visually see that the line of the equation is continuous on both sides, therefor the domain would be x= all real numbers for all possible values of x

Range: To find the range of a function on a graph, measure the extent of the y-values as the function expands.

• Ex: in the graph above, as the graph expands it will eventually cover all possible values of y, for there are no indicated stops or restrictions for the y-values. Therefore y= all real numbers for all possible values of y.

How to write Domain & Range

- In order to communicate what the values for domain and range are, there are two types of ways to present the relationships:

• Interval Notation: list the rules that determine which elements are in a set or not

-[] brackets represent that the value is inclusive within the function

-() parentheses represent that the value is not included in the function

- Exception: when writing that the functions domain or range extends from -infinity to +infinity, parentheses are used

ex.:Domain ( -4, infinity)--> The x-values expand from -4 and onward to infinity, not including -4

     : Range [-4, infinity)--> The y-values expand from -4 and onward to infinity, inclusive of -4

• Set Builder Notation: describes the type of numbers within a set and any restrictions

-restrictions on either the x or y values are presented

-describes the type of values in a set by listing the type of number system:

* Natural Numbers= N

* Rational Numbers= Q

* Integers= Z

* Irrational Numbers=P

* Real Numbers= R

* "equal to" is represented as 'E"

ex.: Domain:  | x E R| 1< x< infinity| = x is equal to all real numbers such that x is greater than 1 but less than infinity. 

-the restriction is: |1<x<infinity|

-the type of number system: |x E R|

      Range: | y E R| -2<y<infinity|= y is equal to all real numbers such that y is greater than -2 but less than infinity.

-the restriction is : |-2<y< infinity|

-the type of number system: |y E R|

Conclusion:

     Domain and Range are important concepts to know for they measure the extent/ possible potential for a function that could model real world examples. Measuring the Domain and Range effectively could demonstrate future growth or paths values can take. Using Domain and Range one can find values to input into functions as well.