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Question 250253: Please help me help my daughter solve this homework problem.
For a car traveling at a constant rate of 60 mi/h, the distance traveled is a function of the time traveled.
a. Express this relation as a function
b Find the range of the function when the domain is [1,5,10]
c What do the domain and range represent?
I am thinking that the expressed function should be something like
f(d) = (60m)h
We can solve b. once we can figure out how to express it as a function.
Thank you for your help.
Found 6 solutions by Theo, ankor@dixie-net.com, scott8148, solver91311, jsmallt9, mathitutor:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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:
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
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! For a car traveling at a constant rate of 60 mi/h, the distance traveled is a function of the time traveled.
:
a. Express this relation as a function; f(t) = distance, t=time in hrs
f(t) = 60t
:
b Find the range of the function when the domain is [1,5,10]
f(t) is the range, t is the domain
f(t) = 60(1)
f(t) = 60 mi
:
f(t) = 60(5)
f(t) = 300 mi
:
f(t) = 60(10)
f(t) = 600 mi
:
c What do the domain and range represent?
domain represents time; range represents distance
:
Answer by scott8148(6628)  (Show Source):
Answer by solver91311(24713)  (Show Source):
Answer by jsmallt9(3758)  (Show Source):
You can put this solution on YOUR website! a. The basic equation that relates distance, rate and time for travel at a constant (or average) speed is: d = rt. To write this as a function for travel at a speed of 60 we would write:
f(t) = 60t
or perhaps
d(t) = 60t
b. & c. Domain is the set of possible values for the independent variable of a function. In other words the domain is the set of possible inputs to a function. The range is the set of possible outputs from a function. Since the outputs of a function are determined by its inputs, one must know the domain of a function to be able to find its range.
A domain of [1,5,10] makes no sense. I am going to assume that it is [1.5, 10]. This notation is called interval notation. Interval notation is a shorthand way to express a contiguous set of numbers. This particular notation says the domain is the set of all the numbers between 1.5 and 10, including 1.5 and 10. (A parenthesis on either end (or both ends) of the notation means the number at that end is not included in the set. So an interval of (4, 20] would indicate all the numbers between 4 and 20, including 20 but not including 4.)
Now that we know the domain we can figure out the range. Since the function f(t) = 60t is a linear function (i.e its graph is a line), then we can find the range by finding the outputs for the endpoints of the domain:
f(1.5) = 60(1.5) = 90
f(10) = 50(10) = 500
So, if the domain is [1.5, 10], the range is [90, 500]
Answer by mathitutor(25) (Show Source):
You can put this solution on YOUR website! (a)The distance travel when something is moving at a constant speed = speed x time
As the constant velocity is given = 60 mi/hr
The distance travel will be varying with time and it is a function of time as given below:
s(t) = 60t where t is in hours.
I think this is what you are looking for. Contact me at tutor@mathitutor.com for any further help.
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