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NationalTutoringObservatory
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MathEd-PII

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volunteer
First, you find the zero of x-2, which is 2. Then you take the coefficients of all the other terms in the equation and write them in this format. Does this look familiar to you?
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student
yes
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volunteer
First, we brought the first coefficient down and did not do anything with it. Then, we multiplied it by 2. This is what would be added to the second coefficient.
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volunteer
Then, we bring down that value and multiply it by two and add it to the next coefficient. We keep repeating this process until the end. 7, the last number on the rectangle is the remainder.
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volunteer
The number before 7 would not have an x, and then the next number before that would have x, and the next number before that has x^2 and so on. The quotient should always be one degree lower than the dividend.
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student
okay
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volunteer
Do you want to do another synthetic division problem or try to learn another concept?
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student
try another problem
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volunteer
Do you want to try solving this on your own first?
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student
yes
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volunteer
You are doing it mostly right. The only mistake is that you have to bring the 4 down by itself. Then you start the series of multiplications
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student
okay, can you show me?
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student
ohh okay i get it
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volunteer
Do you know how to write the quotient and remainder?
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student
not exactly, i think so but it's probably not right
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volunteer
You can try and then we can check
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student
okay
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student
do i use variables or no
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volunteer
You use x in the quotient.
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volunteer
The first term of the quotient should be one degree lower than the divided. If the first term on the dividend is x^4, then the first term of the quotient will be x^3.
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student
can you write it for me so i can see
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volunteer
Do you have any specific questions about the process of synthetic division?
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student
not really
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volunteer
Do you want to do another synthetic division problem or learn another concept?
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student
learn another concept
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volunteer
Which concept are you the most worried about for your test? We can cover that.
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student
all of it but probably the theorems or rational functions
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volunteer
Ok, do you need to know how to graph rational functions for your test?
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volunteer
I can do an example showing graphing.
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student
yes please, just in case
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volunteer
To find the vertical asymptote, we solve the bottom part of the function, in this case X-2. The vertical asymptote is at x=2.
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volunteer
For horizontal asymptotes, there are some special rules. I am going to write them out under the graph.
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student
okay'
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volunteer
When the largest degree of both the numerator and the denominator is the same, you divide their coefficients to find the horizontal asymptote.
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volunteer
If the degree at the bottom of the rational function is greater than the top, the horizontal asymptote is always y=0.
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volunteer
In our original equation, both only has x. So we divide the coefficients, 1/1 to get a horizontal asymptote of y=1.
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volunteer
The next step, after figuring out the asymptotes is to find the x-intercept. To find this, we find the solution to the top of the equation. In X+3=0, X=-3. This is a point we plot on the graph.
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volunteer
Then we draw a graph approaching the asymptotes going through the x-intercept.
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volunteer
Then we draw a graph on the side opposite to it.
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volunteer
Do you have any questions, I know that was a lot of information
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student
not really i think i just need to practice utt
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student
it
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volunteer
Do you want to go over remainder theorem?
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student
umm that's okay i have to go to dance and then i'll come back and start another session to finish the topics, but thank you I really appreciate it
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volunteer
Ok, it was great working with you. Good luck on your test.
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student
thank you
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volunteer
hi StudentA
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[ { "pii_type": "PERSON", "surrogate": "StudentA", "start": 3, "end": 11 } ]
student
hi i need help i have a test tomorrow
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volunteer
on Saturday?
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student
Precalc now pre calc
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student
please help
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volunteer
you'studying, studying?
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student
Precalculus cource
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volunteer
OK
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volunteer
the rules say I shouldn'tutor student, math class is OK, help students anyway, if I can
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student
thank you so much
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student
i need help on difference of quotient and verifying a inverse
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volunteer
wow, that's getting very close to calculus
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student
it is?
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volunteer
yes. difference quotient is almost a derivative, and a derivative is most definitely calculus
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volunteer
let's see the problem
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student
ok ill bring it up
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volunteer
I tutor all math subjects except calculus, and had to look up difference quotient
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student
is there a calculus option on here?
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volunteer
there are 2, I think
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volunteer
but let's see if I can help you
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student
ok
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student
so its f(x)=-^2+5x
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volunteer
-x^2?
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student
wait no sorry
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student
f(x)=-2x^2+5x
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student
this
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volunteer
do you know the formula for the difference quotient?
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student
no
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volunteer
I'll put it on the board
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student
ok
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volunteer
can you guess what to do next?
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student
wait its over that and not h?
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volunteer
the x's cancel and you get h
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student
ohhhh ok
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volunteer
writing it this way shows that you are using x+h and x in both numerator and denominator
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student
ohhhh ok
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volunteer
so, what next?
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student
we should plug in the equation
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volunteer
yes, plug in x+h and plug in x on the top
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volunteer
go ahead
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volunteer
work on the board
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volunteer
good start
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student
what do i do with the 5x
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volunteer
replace x with x+h again
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volunteer
let me make it smaller to give you more room
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student
ok thanks
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volunteer
there
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volunteer
now the -fx)
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volunteer
-f(x)
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student
do i expand the biononiaml
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volunteer
put the -f(x), first
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student
huh where
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volunteer
numerator
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volunteer
f(x+h)-f(x), right?
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