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First. <u>Finding the x-intercepts of </u>
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Let
be the change in water level. So to find the
x-intercepts of this function we can use
The Rational Zero Test that states:
To find the zeros of the polynomial:
We use the
Trial-and-Error Method which states that a factor of the constant term:
can be a zero of a polynomial (the x-intercepts).
So let's use an example:
Suppose you have the following polynomial:
where the constant term is
. The possible zeros are the factors of this term, that is:
.
Thus:
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From the foregoing, we can affirm that
are zeros of the polynomial.
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Second. <u>Construction a rough graph of</u>
Given that this is a polynomial, then the function is continuous. To graph it we set the roots on the coordinate system. We take the interval:
![[-2,-1]](https://tex.z-dn.net/?f=%5B-2%2C-1%5D)
and compute
where
is a real number between -2 and -1. If
, the curve start rising, if not, the curve start falling. For instance:
Therefore the curve start falling and it goes up and down until
and from this point it rises without a bound as shown in the figure below
