Question 250253
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<br>
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.<br>
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 <b>not</b> 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.)<br>
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]