We will first determine domain and range of the function shown below.
V(c) = 98c
Then, we will draw its graph.
Determining the Domain
Because c represents the number of cups of milk the jug can hold, the smallest possible value is c= 0. Notice that c cannot take any negative values, as it does not make sense for a jug to hold negative cups of milk.
0 ≤ c
It is given that the jug can hold 16 cups. That means the maximum value is c= 16, as the jug physically cannot hold more milk.
c ≤ 16
Then, a reasonable domain for this situation is the combination of the above intervals.
Domain: & 0 ≤ c ≤ 16
Determining the Range
We can now use the domain to determine the corresponding range. Since the function is a straight line, the minimum and maximum values of the domain will determine the minimum and maximum range. Let's substitute c=0 and c=16 into the given function rule.
c
98c
V(c)=98c
0
98( 0)
0
16
98 ( 16)
1568
As the minimum and maximum values of V are 0 and 1568, respectively, a reasonable range for this situation is all numbers between these values.
Range: 0 ≤ V(c) ≤ 1568
Drawing the Graph
We know that the points ( 0, 0) and ( 16, 1568) are the minimum and maximum points of the function. Therefore, the graph will be the line that joins these points.
