Point of discontinuity - Rational Functions

Point of discontinuity


• "point of discontinuity" exists when the numerator and denominator have a factor in common.
i.e. (x)=(3x8)(x+5)(2x7)(x+5)(4x+9)(3x+8)(2x7)\left( x \right) = \frac{{ - \left( {3x - 8} \right)\left( {x + 5} \right)\left( {2x - 7} \right)}}{{\left( {x + 5} \right)\left( {4x + 9} \right)\left( {3x + 8} \right)\left( {2x - 7} \right)}} ; points of discontinuity exist at x=5x = - 5 and x=72x = \frac{7}{2} .
• To determine the coordinates of the point of discontinuity:
1) Factor both the numerator and denominator.
2) Simplify the rational expression by cancelling the common factors.
3) Substitute the non-permissible values of x into the simplified rational expression to obtain the corresponding values for the y-coordinate.
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Point of discontinuity

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