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NationalTutoringObservatory
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MathEd-PII

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volunteer
bye.
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student
bye
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volunteer
hello!
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student
hi, I am having problems with my rationals test review
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volunteer
okay great! can you give me an example?
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volunteer
so you have to simplify?
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student
The question for that equation is what is the EBA?
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volunteer
im sorry, can you define EBA?
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student
EBA = end behavior asymptote
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volunteer
ahh i see
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volunteer
so that basically means the horizontal asymptote
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student
Yes, that is the umbrella that the HA is under
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volunteer
okay greay
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volunteer
great*
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volunteer
so let me teach you a little trick
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volunteer
look at the highest degree of numerator and denominator
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volunteer
wait do you want to factor or find the HA first?
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student
I was taught to factor then find HA
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volunteer
okay, lets factor first
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volunteer
so we would objectively want to cancel out the numerator and the denominator
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volunteer
are you familiar with the ac method?
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student
Yes, and the A and M method
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volunteer
okay, i like the ac method so lets do that
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volunteer
so we are left with 3x+1
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student
I just don't know where to go from there
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volunteer
so think about it on a graph
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volunteer
its just a regular line that goes up
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volunteer
as it goes to positive infinity, its going to go up up up
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volunteer
and goes down when going to negative infinity
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student
Yes, how did you get the graph from your factored form?
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volunteer
well the graph i just did is 3x+1
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volunteer
because the (x-5) cancelled out on the numerator and denominator
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student
Ahh, those are your zeros?
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student
That you graphed?
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volunteer
no
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volunteer
its the same thing as f(x) but there is a hole at x=5
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volunteer
if you cancel out the factors, then youre left with the basic graph (3x+1)
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volunteer
okay, lets take a step back
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volunteer
did you understand how i did the ac method, right?
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student
sort of
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volunteer
what part is a bit confusing?
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student
how you got to -15
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volunteer
so the standard form of a quadratic is:
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volunteer
ax^2+bx+c
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student
ok
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volunteer
a in the numerator is 3 and c is -5
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volunteer
so a times c (ac) is -15
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student
ok, that makes a lot more sense. I may have forgotten how to do the ac method . that was s along time ago
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volunteer
yeah,haha me too
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volunteer
but practice just engraved it into my brain
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volunteer
what class is this for again?
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student
pre-cal
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volunteer
okay cool
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volunteer
so lets go back to the problem
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student
ok
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volunteer
so the factors of -15 that make up -14 are 1 and -15
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volunteer
because you add the factors together to get b
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volunteer
-15+1=-14
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student
yes, that is very obvious now
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volunteer
haha, okay so then i expanded the original polynomial into 3x^2-15x+x-5
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volunteer
i think its best to group the biggest number with Sarah because it always works
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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 50, "end": 55 } ]
volunteer
so thats why 3x^2 and -15x are togehter
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student
ok
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volunteer
what is the largest common factor between those two terms?
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student
5
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volunteer
no, 5 is not a factor of 3x^2
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student
3x
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volunteer
yes!
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volunteer
so then you group it as i did on the board
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volunteer
so it looks like 3x(x-5)
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student
and then you devid
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volunteer
not yet
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volunteer
because you need to group it
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volunteer
since we already have (x-5) of the other side, we can add what is multiplying (x-5) together to make it a term itself
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volunteer
so 3x(x-5) +1(x-5)
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volunteer
we can just add the outsides
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student
ok
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volunteer
3x+1
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volunteer
yes
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volunteer
and thenn you can divide
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volunteer
(3x+1)(x-5)/(x-5)
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volunteer
is just 3x+1
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student
ohhh, then you set 3x+1 equal to 0?
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volunteer
you do not need to set anything equal to zero
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student
well how did you get the point on the graph?
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volunteer
oh for the graph? i guess so
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volunteer
but the graph isnt too revelant, it was just to help you visualize
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volunteer
but just think about y=3x+1
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volunteer
and then thats the graph
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student
ok, I understand
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volunteer
okay, so using the graph to help you visualize, what are the end behaviors?
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student
down, up
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volunteer
could you explain
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student
that would be the end behavior?
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volunteer
yes!
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volunteer
okay
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volunteer
do you wanna see an easier way?
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student
yes!!!!!!
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volunteer
okay
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volunteer
can you erase the part under the function
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