Playing with Graphs --- 2

Calculus Level 4

\[ \large{ f (x) = \frac{(x - \alpha)(x - \beta)}{(x - \gamma)(x - \delta)}} \]

You are given the function \(f(x) \) as described above where \( \alpha , \beta , \gamma\) and \( \delta \) are distinct real numbers.

Find the probability that the function formed is always increasing or always decreasing at any point on its graph.


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