What is the difference between domain and range? Describe a real life situation that could be modeled by a function?

Question

Describe the values for x that may not be appropriate values? A function could, for example, indicate the amount of bone strength (y) in a living human body over time in years (x). It would not make sense to look at negative years, because the person would not yet be born. Likewise, looking beyond 200 years might not make sense, because many people do not live to be 200.

Answer 1

 Domain is the set of discrete or continuous numbers  that independent variable can take, to have a valid value for dependent variable, in functional relation with dependent variable.

 

    For example  Y = 2x +3  x can take any real value quantity to have a valid value for Y

       So domain is written in the form of

 

            -∞< x<+∞  or xε (-∞, +∞)

       Range is the value that  Y can take in functional value, in this case will be the same as domain:  

             

               -∞< x<+∞ or xε (-∞, +∞)

 

    If there is function Y = 1/X

 

        x = 0 , y becomes undefined So Domain is

 

           -∞ <X < 0 Or  0<X <+∞,  Y = 1/x will have the same range.

 

         Now Consider:

    

              Y = X² - 2X + 5 = ( X - 1) ² + 4 

 

                    Domain :  x ε (-∞, +∞)

                   Here x=1, y= 4 is the minimum value of: therefore:

                   Range:

                                Xε[ 4, +∞)