Quick Easy Question: Point of Discontinuity

[Dooga Blackrazor]

I have been doing some function questions. I think it is Calculus because it is in a Calculus course; however, it could be pre-calculus. I decided to post it here anyway. Question:

(x+5)(x+4)
___________
(x+4)

Every question I have done involve a POD like this. Two on the top and one on the bottom that cancels out. POD = -4 and is a circle on the graph. At a y component and x = -4. The point doesn't go through there.

Is every POD situation end up looking like that. I don't know what POD even means, lol. Thanks.

 

[Fermat]

... I don't know what POD even means, lol. Thanks.

Couls it be: Point Of Discontinuity ?

 

[HallsofIvy]

Since the original post used the term "point of discontinuity" in the title, I suspect the poster knew that "POD" meant "point of discontinuity" but doesn't understand what "point of discontinuity" means.

In this particular case, as long as x is not -4, we can cancel the two "x+4" terms and the y= (x+5)(x+4)/(x+4)= x+ 5. The graph of y= x+5 is a straight line, in particular, containing the point (-4, 1). You can draw it in one continuous motion.

The graph of y= (x+5)(x+4)/(x+4) looks exactly like that except that now y is not defined when x= -4 ((1)(0)/0 is not 1- it is undefined). The graph of that function is a straight line with a "hole" (perhaps represented by a circle) at (-4, 1). It is not a single "continuous" line- there is a "discontinuity" at (-4, 1) which is why it is called "POD"- "point of discontinuity".