The amount of juice you drink is represented by j.
The height of juice in the bottle is represented by h.
The beginning amount of juice is 20ounces.
Before we graph the function rule, let's make a table of ordered pairs. We know that the bottle contains 20ounces. This amount can only decrease as the juice is drank and can never become a negative number, so only j values between 0 and 20 are reasonable.
0≤ j ≤ 20
To keep our table from getting too big, let's use intervals of 5ounces.
j
h=6-0.3j
(j,h)
0
h=6-0.3( 0)
(0,6)
5
h=6-0.3( 5)
(5,4.5)
10
h=6-0.3( 10)
(10,3)
15
h=6-0.3( 15)
(15,1.5)
20
h=6-0.3( 20)
(20,0)
Based on our table, we see that the starting height of the juice in the bottle is 6inches. This height can only decrease and can never become negative, so it only makes sense to include values from 0 to 6 in our graph.
0≤ h ≤ 6
Let's plot our points and connect them with a line.
Note that, we would not necessarily drink exactly 5.0fl. oz every time we drink from a bottle but instead could drink any amount of the 20ounces at a time. Because every value between 0 and 20 is possible, every height between 0 and 6 is also possible, which means that the function is continuous.
