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Intervals of constant signs of a function

The model demonstrates intervals where a function f(x) = sqrt(x2-5x+6)/(x-5) is negative.

Note that x2-5x+6 = (x-2.5)2-0.25 and is negative on (2; 3). Thus the f(x) is not defined on this interval.

A square root function is positive. Consequently the sign of f(x) is the same as the sign of x-5 except x=5 where 1/(x-5) is undefined.

The f(x) is negative if x belongs to a union of intervals (-?; 2) and (3; 5).

The model is a movie. To navigate through the movie use Play, Pause, Stop, Previous step and Next step buttons.

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