The volume of water in a tank is modeled by the function y = 1.15x3 – 0.1x2 + 2 where x is the number of minutes after the fauce
2 answers:
Given:
The volume of water in a tank is modeled by the function
where, x is the number of minutes after the faucet filling the tank is turned on.
To find:
The y-intercept and what does it represent in this context?
Solution:
We have,
Substituting x=0, we get
Therefore, the y-intercept is 2 and it represents the volume of water in a tank before the faucet filling the tank is turned on.
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First. The function is defined only for
as shown in the Figure. This is also true because of 
where 
must be greater (or equal) than zero.
Second. The range of the function are the values of
.
Third. If creases then 
always creases, too.
So if we graph this function we will get the Figure below. Thus, let's study both the equation and the graph to get some conclusions. Therefore, we can assure these statements:
First. The function is defined only for
Second. The range of the function are the values of
Third. If