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The function m=30-3r represents the amount m (in dollars) of money you have after renting r video games.

Find the domain and the range of the function. Is the domain discrete or continuous? Explain.

Respuesta :

Yna9141
The domain of the equation are all the possible values of the independent variables that would make the equation reasonable, possible or true. In this item, the independent variable is r. This could take a value of 0 up to the point when m is equal to zero.
        m = 30 - 3r = 0
              r = 10

The domain is therefore [0, 10]. 

The range is the value of the dependent variable which would be from 0 to the point when no video game is played. This is, [0, 30]. 

The function is discrete because r and m cannot take every value in the number line. 

Domain and Range of the function are  [tex][0, 10] \; \&\; [0,30][/tex] and it is a discrete function.  

Explanation:

Given: The function [tex]m=30-3r[/tex] represents the amount [tex]m[/tex] (in dollars) of money you have after renting [tex]r[/tex] video games.

According to question,

Function is  [tex]m=30-3r[/tex].

Domain of function is calculated as [tex]30-3r=0[/tex]

                                                                 [tex]-3r=-30\\[/tex]

                                                                     [tex]r=\frac{-30}{-3} \\r=10[/tex]

Domain of function is [tex][0, 10][/tex].

Now, range of the function is the value which is dependent variable on domain of the function.

Range of the function is [tex][0,30][/tex].

Here, The given function  [tex]m=30-3r[/tex] is discrete because the values of  [tex]r[/tex] and [tex]m[/tex] cannot take every value in the number line.

Therefore, Domain and Range of the function are  [tex][0, 10] \; \&\; [0,30][/tex] and it is a discrete function.  

Learn more about domain and range of the function here:

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