Is the function f(x) = (x - 1)/((x - 2)(x - 8)) continuous.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function f(x) = (x - 1)/((x - 2)(x - 8)) has two terms in the denominator (x - 2) and (x - 8) which equal to 0 at x = 2 and x = 8 respectively.

Look at the graph of the function:

At x = 2, as the values of x approach from the left, the value of f(x) is tends to `oo` . And as x = 2 is approached from the right the value of f(x) tends to `-oo` . Similarly, at x = 8, approaching the from the right the value of f(x) tends to `oo` and approaching from the left, the value tends to `-oo` .

At the points where x = 2 and x  = 8, the function is discontinuous. This discontinuity is referred to as asymptotic discontinuity.

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