Learn how to identify the discontinuities as removable or non removable

👉 Learn how to find the removable and non-removable discontinuity of a function. A function is said to be discontinuous at a point when there is a gap in the graph of the function at that point. A discontinuity is said to be removable when there is a factor in the numerator which can cancel out the discontinuous factor and is said to be non-removable when there is no factor in the numerator which can cancel out the discontinuous factor.

To find the discontinuities of a rational function, it is usually useful to factor the expressions in the function and we then set the denominator equal to 0 and solve for x. The value of x for which the factor appears in both the numerator and the denominator is the point of removable discontinuity while the value of x for which the factor appears in only the denominator is the point of non-removable discontinuity.

Organized Videos:
✅ Find the Asymptotes of Rational Functions
✅ Find the Vertical and Horizontal Asymptotes of a Rational Function y=0
✅ Asymptotes of Rational Functions | Learn About
✅ Find the Asymptotes of a Rational Function with Trig
✅ Find the Asymptotes and Holes of a Rational Function
✅ Find the Slant Asymptotes of the Rational Function

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[chaks]

The removable value is x=-1, the non removable is x=1

[angelmendez-rivera]

Here is something that may be insightful: if you graph the curve y = 1, you will just see it is just a straight horizontal line. If, instead, you graph y = x/x, then the curve is almost identical, except it is missing the point at x = 0 to avoid division by 0. This is what creates the hole. So if I multiply f(x) by x/x and I graph y = x/x·f(x), I will just get the graph of y = f(x) with a hole at 0, because multiplying by x/x is a lot like multiplying by 1, except at the point where the hole is located. If I replace x/x by (x – c)/(x – c), then the hole occurs at x = c. This why removable singularities work the way they do, and why they produce no asymptotes.

[rkssk]

thank you good sir you're saving my grades rn (also glad i caught the correction from the pinned comment woohoo :D)

[duffharrold]

Asymptopes again....is it just me? He writes "totes" but says "topes". Maybe I'm wrong.