Datasets:
NationalTutoringObservatory
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MathEd-PII

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student
Have a great rest of your day
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student
Bye
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student
Hello
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volunteer
Hi
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student
How are you?
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volunteer
I'm fine, how are you?
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student
I'm doing well
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volunteer
Just a min
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volunteer
Ok so are you familiar with what domain and range is
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volunteer
or should we go with a recap?
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student
sure
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volunteer
So domain can be thought of as the input set (group of values) of a function. Basically, all those values which can be inputted into the function to get a valid (defined) output
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volunteer
So basically to check the domain, we would just look at the x-axis to see for what values of x is f(x) defined
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volunteer
Can you have a go at the example using this?https://mathhelper.com/question1y question 1 part A
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[ { "pii_type": "URL", "surrogate": "https://mathhelper.com/question1", "start": 44, "end": 76 } ]
student
yep
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volunteer
you've made a slight mistake in part A
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student
what is it
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volunteer
at x=5 the function is not defined so you have rightly used an open interval but what about at x=-1?
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student
oh
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student
[
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volunteer
yeah
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volunteer
same with your range
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volunteer
perfecy
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volunteer
*t
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volunteer
you've switched up the answers
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student
wait for x intercept do u not make y = 0
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volunteer
an x-intercept is the point where the function intersects the x-axis
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volunteer
yes
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volunteer
look at x=3
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student
i see
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volunteer
no that's the same mistake again
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volunteer
ok look at x=3
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volunteer
so what axis do you see it intersecting
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student
what do you do to find x-intercept
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student
set y = 0?
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volunteer
yes
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student
and to find y intercept set x = 0
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volunteer
yes
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student
i understand it now
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volunteer
yeah, perfect
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volunteer
Any other questions?
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student
yerp
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volunteer
ok yeah i can see it now
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student
zeroes is the same as x intercept right coach?
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volunteer
yeah
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student
find zeros make y = 0
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volunteer
yes
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student
L math
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volunteer
👍
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student
do you just say x = 20/3 or
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student
(20/3, 0)
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volunteer
both are correct, but I'd recommend the second one
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volunteer
alright what about y-intercept
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student
one sec
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student
so y intercept set x = 0
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volunteer
yes
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volunteer
excellent
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volunteer
have a go at the second one
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volunteer
yup
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volunteer
last one
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volunteer
you forgot to divide the 2 when solving for x
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student
um
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student
whoops
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volunteer
the rest is corredct
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student
so umm
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volunteer
one min
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volunteer
Alright so go ahead, I'll check
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student
um
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student
i dont rly know this ngl
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volunteer
ok Ill help you out
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volunteer
so if the function is symmetric about the x-axis, then for every value of x, I should have two values of y
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volunteer
y and -y
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volunteer
right?
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student
so a parabola
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volunteer
not necessarily, look at the first graph itself
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volunteer
its symmetric, but isnt a parabola
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student
hmm
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volunteer
so basically I can say that f(x) = y = -y
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student
so what would i call dat
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volunteer
that would be your algebraic test
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volunteer
basically you can replace all the y's in the equation with -y's and the equation would remain the same
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student
so the other one is f(x) = x = -x
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volunteer
no not exactly, just a min, we'll come to the second one just make a note in the first
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volunteer
you can't call this a function, so I would avoid writing f(x)
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student
why cant u call it a function
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student
isnt that just a prabola
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volunteer
the definition of a function is that for each value of x there can only be one value of y, if you are familiar with mapping and the concepts of sets, I could make it clearer but otherwise we can ignore that for now
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volunteer
just remember, if you see one x value giving you more than one y-value, the graph isnt a function
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volunteer
So a rather better way of phrasing the algebraic test is y and -y give same value of x, or that the rq remains the same
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volunteer
if you are familiar with the modulus function, you can identify graph 1 too(as an extra)
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volunteer
ok getting back to point, any questions in the algebraic test?
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student
how do i confirm algebriaclly
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volunteer
replacing y with -y in the equation of the graph does not change the equation
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volunteer
Now we can move on to the second graph
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volunteer
You there?
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volunteer
Any questions?
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student
yeah
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student
just kinda lost
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volunteer
alright let's get back on track then
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volunteer
so we need to algebraically prove that a graph is symmetrical about the x-axis
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