What are the asymptotes and removable discontinuities, if any, of #f(x)=(1 - 4x^2) / (1 - 2x)#?

1 Answer
Roella W.
Dec 30, 2015

The function will be discontinuous when the denominator is zero, which occurs when #x=1/2#
As #|x|# becomes very large the expression tends towards #+-2x#. There are therefore no asymptotes as the expression is not tending towards a specific value.

The expression can be simplified by noting that the numerator is an example of the difference of two squares.
Then
#f(x) = ((1-2x)(1+2x))/((1-2x))#
The factor #(1-2x)# cancels out and the expression becomes
#f(x) = 2x + 1# which is the equation of a straight line. The discontinuity has been removed.

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