Question 250253
rate * time = distance is the basic equation you have to work with.


the function is D = R*T where D = distance, R = rate of travel, T = time.


It would not be f(D), because then D would have to be the argument of the function and the arguments of the function are R and T.


They are giving you R as 60 mph, so that becomes a constant in your function rather than a variable.


your equation becomes D = 60*T


to write this in functional notation, you would say:


D = f(T) = 60*T


This means D is a function of T with the function expressed as 60*T.


T is the argument of the function.


60 * T are the rules establishing the relationship between T and D.


T is the independent variable.


D is the dependent variable because it depends on the value of T.


When the domain is [1,5,10], the range is [60*1,60*5,60*10]


When T = 1, f(T) = 60*1 = 60
When T = 5, f(T) = 60*5 = 300
When T = 10, f(T) = 60*10 = 600


The domain represents the amount of time traveled.  The assumption is that it is in hours although that was not stipulated.


The range represents the distance traveled.  That would be in miles.


A graph of your equation would look like this:


{{{graph(600,600,-5,15,-100,700,60*x,60,300,600)}}}


the horizontal lines represent the range of the function.


vertically down from that intersecting with the x-axis are the domain of the function.


you can see when T = 1, f(T) = 60, when T = 5, f(T) = 300, when T = 10, f(T) = 600