why is my sign of a function wrong ? , seems like that I just dont know how to use this method , so does anyone know this method
#sign of a function
brittle python
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why is my sign of a function wrong ? , seems like that I just dont know how to u...
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delicate night
why is my sign of a function wrong ? , seems like that I just dont know how to u...
It would be easier to notice that x^2 - 3x + 2 = (x - 1)(x - 2).
So, f(x) = √(x - 1) for x ≠ 2.
delicate night
Because we can only have (x^2 - 3x + 2)/(x - 2) = x - 1 when x ≠ 2. Otherwise we get 0/0, which is not good.
brittle python
okay , I never did this method so I might try to learn it , but why in this case is my method wrong ?
delicate night
The function won't change sign when going across x = 2.
brittle python
but then I would get
-|-
instead of
-|+
which still would be wrong since it would need to go to +|+
and shouldn't everything sqrt(x)>= 0 so it should start from + change on 1 =>- change on 2 => +
delicate night
but then I would get
-|-
instead of
-|+
No, it will be - for x < 1, + for 1 < x < 2 and + for x > 2.
slow field
https://www.wolframalpha.com/input?i=Plot+sqrt%28+%28x%5E2-3x%2B2%29%2F%28x-2%29...
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slow field
,w Plot sqrt( (x^2-3x+2)/(x-2) )
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delicate night
As I said, it's √(x - 1) for x ≠ 2.
brittle python
As I said, it's √(x - 1) for x ≠ 2.
Okay is this correct
delicate night
Yes, but again, easier to factor the numerator first and cancel, just minding that x ≠ 4.
brittle python
okay I will def do that after I just learn why this method is not working rn , so I dont feel like I wasted time learning it
leat me just do the sqrt version of this problem
and see where my logic breaks exactly
delicate night
okay I will def do that after I just learn why this method is not working rn , s...
Note the following: if (x - x0)^n has an even power n (which includes 0, like in your cases), then the sign doesn't change when passing through it.
brittle python
so the sign should not change when doing sqrt() of something (+)
and sqrt should always be positive number so it should always be + ?
that is at least what I heard
delicate night
so the sign should not change when doing sqrt() of something (+)
No, the root doesn't have anything to do with that.
brittle python
No, the root doesn't have anything to do with that.
brittle python
Okay is this correct
okay I followed exactly the same rules as I did here
where did I make a mistake ?
I was told that if its sqrt I should write + in the whole row
bc sqrt is always positive
and then it would be actually something that looks like a answer
delicate night
Not sure what you're doing there.
We have (x^2 - 3x + 2)/(x - 2) = x - 1 for x ≠ 2. So:
- for x > 2
- for 1 < x < 2
- for x < 1
Which is as expected.
Clearly, the root can't be negative.
delicate night
Abandon the root. It doesn't need to be there.
Method of intervals applies to rational functions.
brittle python
Method of intervals applies to rational functions.
1.but isnt this correct ? I would like to at least know how they got the solution to this in this way
2.what does that mean
in this case it looks like it is correct
