a What is the cost if no water at all is consumed? What is the cost for the first 100 cubic feet? When does the price for 100 cubic feet of water increase?
B
b How do you determine if a relationship is a function or not?
C
c The domain is the set of all input values for which a function is defined. The range is the set of all the output values.
a In order to drawn the described graph, we should first recognize that it is a step function. Therefore, we need to sketch the graph in intervals. When no water is used, the cost will be the service fee only, $12.70. For the first 300 cubic feet of water, the cost will increase by $3.90 for each 100 cubic feet.
After the first 300 cubic feet of water has been consumed, the price for the water is raised. Each additional 100 cubic feet then costs $5.20. Let's add this to the graph.
b For graph to be a function, there can only be one output value for each input value. We can test this using the Vertical Line Test. Therefore, yes, this is a function.
c
The domain is the amount of water consumption for which the function is defined. In this case the smallest possible volume is 0 cubic feet and the greatest is 1000 cubic feet.
0≤ V ≤ 1000 cubic feet
The range is the set of all possible costs for the predicted water consumption for a month. The lowest possible cost is only the service fee, $12.70. The cost then jumps first with $3.90 for each 100 cubic feet. After 300 cubic feet has been consumed the cost will jump with $5.20 for each 100 cubic feet. Let's calculate the possible costs for consumption of up to 500 square feet of water.
Volume
Water Cost + Service Fee
Total
V = 0
12.70
$12.70
0< V ≤ 100
3.90(1) + 12.70
$16.60
100< V ≤ 200
3.90(2) + 12.70
$20.50
200< V ≤ 300
3.90(3) + 12.70
$24.40
300< V ≤ 400
3.90(3) +5.20(1) + 12.70
$29.60
400< V ≤ 500
3.90(3) +5.20(2) + 12.70
$34.80
By continuing these calculations we can find the range for the function, which is the set of all possible costs.
Range: { &$ 12.70, $ 16.60, $ 20.50,
&$ 24.40, $ 29.60, $ 34.80,
&$ 40, $ 45.20, $ 50.40,
&$ 55.60, $ 60.80 }
