Graph difference

[pinkman]

Joe, don't be so rude!
Hi dmusic, welcome back! Joe is true, you've been a bit confusing.

(05-01-2018 01:45 AM)Joe Horn Wrote:  (1) That's not an equation.

True, it's an expression. But like any calculator, you could have infer the missing '=0'

(05-01-2018 01:45 AM)Joe Horn Wrote:  (2) Your comment #2 indicates that you meant the denominator to be X^2+5X (which is the way it was typed into HP's calculator forum and into your HP Prime), not X^2-5X.

Yes dmusic we think you made a mistake somewhere, but we still understand the question.

For the expression f(x)=(X^2 - 25) / (X^2 - 5*X), there is only 1 root (f(x)=0) at x=-5, not at x=5.
There is a discontinuity at x=5, the calculator does not have any other mean to show it than with a vertical bar, but it is not a root, the limit is 2 (try with x=4.999 or x=5.001).

For the expression f(x)=(X^2 - 25) / (X^2 + 5*X), there is only 1 root (f(x)=0) at x=5, not at x=-5. There is also a discontinuity at x=-5, the limit is also 2 (try x=-4.999 or x=-5.001)

(05-01-2018 01:45 AM)Joe Horn Wrote:  (3) Both apps' graphs show the root to be at X=5, not at X=0.

Yes dmusic, finding the root of a function means finding f(x)=0, so (X^2 - 25) / (X^2 - 5*X)=0, which is true for (and only for) x^2-25=0 => x^2=25 => x=-5 but not x=5 because of the denominator.
For (X^2 - 25) / (X^2 + 5*X)=0 it is the opposite : x=5 is a root, x=-5 has no value.

(05-01-2018 01:45 AM)Joe Horn Wrote:  (4) The vertical line at X=-5 is the Advanced Graphing app's way of indicating a removable singularity. It does not indicate another root. Try Y=(X^3-X)/(X^2-1) to see another example of this in action.

There is a discontinuity at x=5 or x=-5 (depending on the expression you used), and the calculator does not have any other mean to show it than with a vertical bar, but it is not a root, the limit is 2 in both cases.

(05-01-2018 01:45 AM)Joe Horn Wrote:  (5) Yes, the Function app differs from the Advanced Graphing app. This is intentional. If they were identical, there would be no reason to have both.

To be more precise, the advanced app refines the graph around specific values like the discontinuity in your case. It also has a more precise way of plotting functions, find values with cursor, and you can enter any kind of expressions, not only functions, eg. y^2 = 1 - x^2 (see attached pictures)