Respuesta :
Answer:
The domain of the function is {0, 1, 2, 3, 4, 5, 6, 7,...,}
The range of the function is {0, 5, 10, 15, 20, 25,...,}
Step-by-step explanation:
Consider the provided information.
Hans opens a new video game store and pays the gaming companies 5.00 for each video game he buys from them. The amount Hans pays is given by f(x) = 5x, where x is the number of video games purchased.
We need to find the domain and the range of the function.
The domain is the set of input values which a function can take, or the domain is the set of all possible x values.
Range: Range is the set of output value produce by the function, or the range is the set of all possible y values.
The number of games Hans buys must be a whole number.
Thus, the domain of the function is {0, 1, 2, 3, 4, 5, 6, 7,...,}
The amount Hans pays is given by [tex]f(x) = 5x[/tex]
For 0 games he need to pay [tex]f(x) = 5(0)=\$0[/tex]
For 1 game he need to pay [tex]f(x) = 5(1)=\$5[/tex]
For 2 game he need to pay [tex]f(x) = 5(2)=\$10[/tex]
Here, we can observe that the output value is the multiple of 5.
Hence, the range of the function is {0, 5, 10, 15, 20, 25,...,}
The determines defines the extent to which a function is applied, therefor, the domain defines the scope of the function.
- The domain of the function f(x) = {x | x ∈ W}
- The range of the function = {0, 5, 10, 15, 20, 25...∞}
Reason:
The given parameters are;
Amount paid for each video game bought = 5.00
The function that gives the amount Hans pays for 'x' video games, f(x) = 5·x
The number of video games Hans buys = x
Required:
The domain and range of the function.
Solution:
The domain are the possible input or x-values.
The number of video games can only be whole number, W, values.
Therefore;
The domain = {x | x ∈ W}
The range of the function are the possible output values
Therefore; the range f(x) = {0, 5, 10, 15, 20, 25...∞}
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