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NationalTutoringObservatory
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MathEd-PII

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student
Ok
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volunteer
we can see that |y+2| - |y-2| will lead to x being 2 or -2 past y = 2 and -2
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student
Okay makes sense
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volunteer
Basically with this problem it's best to simplify and then plug in values near the point specified
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volunteer
for problem 2 we can compare rate of change.
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volunteer
Using the y_2-y_1/x_2-x_1 for slope
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volunteer
We can plug in and see that we get slope = N - 0 / -1.1-(-1)
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volunteer
or N / -0.1
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student
N can’t be negative and can’t be zero so B CD automatically are eliminated
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volunteer
absolutely!
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student
Okay that one was easy
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volunteer
So with -0.1 in the denominator we get this one
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volunteer
It's been a while since I've done parametrics so I might need a moment
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student
It’s okay
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volunteer
Okay so first step would be to get t, so we can sub in x = t
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volunteer
we then get y * e^t = 3, and simplifying, we can get y = 3/e^t
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volunteer
so, with x = t and y = 3/e^t
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volunteer
x has a slope of 1 (with x = t) and y is a negative exponential
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volunteer
Thus y will have a negative slope
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volunteer
I posted an image of the parametric
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volunteer
For most of the parametric problems, it'll ask either to analyze the x and y components
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student
Oh okay
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student
Thank you
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volunteer
btw are you comfortable with isolating equations for the x and y components for parametrics
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student
Can you give me an example
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volunteer
Let's say I want you to give me the equation y = x^2 in the form of (x(t), y(t)))
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student
I will make x equal to t
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student
And since y equals x squared then it’s turned to y equals t squared
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volunteer
nice
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volunteer
For ap precalc I think for parametrics the most difficult part is knowing how to find the x and y components
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volunteer
past that when you have them isolated you can often just look at the components individually for what the problem's asking for
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student
Okay
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volunteer
for example a circle, x^2 + y ^2 = r, it adds in trigonometry when getting the x and y components
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student
An ellipse too
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volunteer
it'll look something like x = rcos(t), y = rsin(t)
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volunteer
yeah
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volunteer
ap precalc is mostly an algebra review course of calculus
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volunteer
So a lot of practice is good
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student
I am going to take calculus in a week for my sophomore year … is it hard
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[ { "pii_type": "GRADE_LEVEL", "surrogate": "sophomore", "start": 45, "end": 54 } ]
volunteer
I would say if you got the fundamentals for algebra down it'll be pretty light for the first half
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volunteer
Derivatives and limits are very similar to the rest of algebra
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student
Oh okay
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volunteer
There's some really good sources online
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volunteer
I would recommend youtubers like blackpenredpen
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volunteer
he posts videos like doing 100 derivatives, integrals, precalc equations, etc
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volunteer
and he explains the concepts really well
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student
Oh wow
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student
Thank you so much
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volunteer
Will that be everything today?
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student
Yes
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student
Thank you so much
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student
You really helped me a lot
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volunteer
No problem, have a good day!
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student
You too
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student
Hello
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volunteer
Hello, how is it going?
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volunteer
What can I help you with today?
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student
I need help with the problems on the board
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volunteer
Okay.
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volunteer
Which part are you confused on?
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student
How to find the correct answer..?
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volunteer
First, tell me what a domain is.
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student
Al the x values
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student
*All
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student
..hello?
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volunteer
Hi, sorry.
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volunteer
Yes, that is correct.
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volunteer
Now, for the first question, what are all the x-values possible?
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student
I’m not sure
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volunteer
Where does the graph start and end (on the x-axis)?
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volunteer
Which number?
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student
The greatest is 6 and the lowest is -5
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student
In x value
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volunteer
Correct.
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student
*s
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volunteer
So, technically the range is from -5 to 6. But, we need to account for any open circles within the range.
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volunteer
Are there any?
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volunteer
We can also eliminate choices a and b, since those are the not the correct numbers.
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student
Ok
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student
There’s two open circles
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volunteer
We won't consider open circles that start the function. Only those that are within the function.
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volunteer
In this case, there is only one.
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volunteer
Which number is it at?
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student
-4,2
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volunteer
Or just -4, we only need the x-value.
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volunteer
Now, we can determine what the domain is.
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volunteer
An open circle means paranthesis, while a closed circle means brackets.
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volunteer
Can you determine the domain now?
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student
What doe the -4 do
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student
*s
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student
*es
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volunteer
It's a hole in the graph, meaning it doesn't exist as part of the domain.
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student
So does it affect the notation..?
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volunteer
It still does affect the notation, yes.
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volunteer
Look at answer choices c and d
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volunteer
They end with -4 (for the first part) and start with four (for the second part).
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volunteer
This indicates that -4 is restricted from the domain, but is still included in the notation.
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student
What do you mean that it starts and ends with four?
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volunteer
(-5, -4) U (-4, 6]
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volunteer
(-5, -4) - this ends with -4.
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