Given a polynomial and a point
, we have that
We know that our cubic function is zero at -4, 0 and 5, which means that our polynomial is a multiple of
Since this is already a cubic polynomial (it's the product of 3 polynomials with degree one), we can only adjust a multiplicative factor: our function must be
To fix the correct value for a, we impose :
And so we must impose
So, the function we're looking for is
Answer as a compound inequality:
Answer in interval notation: [-4, 2)
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Explanation:
The range is the set of all possible y outputs of a function. When dealing with a graph like this, we just look at the highest and lowest points to determine which y values are possible.
The lowest point occurs when y = -4. We include this value. So far we have which is the same as
The upper ceiling for the y value is y = 2. We can't actually reach this value because of the open hole at (-3,2). So we say that
Combine and
to get the compound inequality
This says y is between -4 and 2, including -4 but excluding 2.
To convert this to interval notation, we write [-4, 2) where the square bracket says to include the endpoint and the curved parenthesis says to exclude the endpoint.