Answer:
See below
Step-by-step explanation:
Fiona has a function that shows the amount of money she has to pay ( f(.) ) as a function of the gas the buys (g). So, the function can be written as: f(g). As each litter costs $2.25 we can say that:
f(g) = 2.25g
Lets try to find put which constraints the function f(g) has in its domain, it is, what are the restrictions for the values of g.
Is evident that g cannot be negative, as one cannot buy negative liters of gasoline. We can buy any positive amount of gasoline, doesn't matter if it is an integer number or not. it is possible to buy 5 liters and also to buy 5.45454545545454 liters. A zero amount of liters is also possible, having zero cost.
Thus, as any positive or zero value is positive, but negative values are not, we can restrict the domain to every non-negative real number:
Domain(f) = [0, infinite ) or
Domain(f) = Real non negative
The domain of a function is the set of input values, the function can take.
The domain of the function is: [tex]\mathbf{[0,\infty)}[/tex]
The rate is given as:
[tex]\mathbf{Rate = 2.25}[/tex]
Represent the gallon of gas with x.
So, the amount of gas, as a function is:
[tex]\mathbf{f(x)=Rate \times x}[/tex]
Substitute 2.25 for Rate
[tex]\mathbf{f(x)=2.25 \times x}[/tex]
[tex]\mathbf{f(x)=2.25x}[/tex]
The amount of gas cannot be negative.
So, the domain of the function is: [tex]\mathbf{[0,\infty)}[/tex]
Read more about domain at:
https://brainly.com/question/21853810
