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September 9th, 2017, 06:51 PM   #1
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graphing

Hi guys,
How can I graph this, please teach me.

question: graph (x^2+x-20) / |x-4|
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September 9th, 2017, 07:48 PM   #2
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$$\frac{x^2+x-20}{|x-4|}\equiv\frac{(x-4)(x+5)}{|x-4|}$$

Since the denominator is zero at x = 4, we have a singularity there but it's removable, as the
numerator has a factor of x - 4. Now plot x + 5 and -x - 5, using various values for x, on the
same axes with a "hole" (hollow circle) at x = 4, then join the dots with a line. There are two
branches, one with negative slope (-x - 5) and one with positive slope (x + 5), so be mindful
of where the function "jumps" between branches (at x = 4). Don't forget to title and label your
graph accordingly.
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September 10th, 2017, 12:55 AM   #3
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Quote:
Originally Posted by greg1313 View Post
Since the denominator is zero at x = 4, we have a singularity there . . .
I take it you mean "potential singularity", but see below.

Quote:
Originally Posted by greg1313 View Post
but it's removable, . . .
What makes you think that? It's not.
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September 10th, 2017, 05:45 AM   #4
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I simply failed to give it due consideration.
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