What does 'infinite discontinuity' mean?Context: "In the function 1/[(x+3)(x-2)], there is are infinite discontinuities at x=2 and at x=3"

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beckden | High School Teacher | (Level 1) Educator

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Infinite discontinuity means the function goes to infinity at that point.

The two points for your function are x=-3 and x=2.

We can see which direction the discontinuity goes by making a sign chart.

x<-3  1/((x+3)(x-2)) is 1/((-)(-))=+

-3<x<2 1/((x+3)(x-2)) is 1/((+)(-))=-

x>2 1/((x+3)(x-2)) is 1/((+)(+))=+

So on the left of -3 the function goes to positive infinity,

On the right of -3 the function comes from negative infinity

On the left of 2 the function goes to negative infinity

On the right of 2 the function comes from positive infinity.

If you graph the function you might see the idea better.