Given the limitations of the tank, what is the domain?
Domain: 0 ≤ x ≤ 17 Range: 0 ≤ x ≤ 544 Graph:
Practice makes perfect
We will first determine domain and range of the function shown below.
d(x) = 32x
Then, we will draw its graph.
Determining the Domain
Because x represents the number of gallons of gasoline the consumed by the car, the smallest possible value is x= 0. Please note that the car cannot consume a negative amount of gasoline, so our minimum value for x is 0.
0 ≤ x
It is given that the car has a 17 gallon fuel tank. That means the maximum value is x= 17, as the car physically cannot hold more gasoline.
x ≤ 17
Then, a reasonable domain for this situation is the combination of the above intervals.
Domain: & 0 ≤ x ≤ 17
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. We can substitute x=0 and x=17 into the given function rule.
x
32x
d(x)=32x
0
32( 0)
0
17
32( 17)
544
As the minimum and maximum values of d are 0 and 544, respectively, the corresponding range for this situation is all numbers between these values.
Range: 0 ≤ d(x) ≤ 544
Drawing the Graph
We know that the points (0,0) and (17,544) are the minimum and maximum points of the function. Therefore, the graph will be the line that joins these points.
