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NationalTutoringObservatory
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MathEd-PII

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student
yes :)
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volunteer
OK, let me know if you can hear me.
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student
I can
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volunteer
OK, that's good. So basically for this equation,
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volunteer
we can see over here, um, I'm gonna annotate, OK, so we can see GFX is this, OK, we're gonna do different colors. GFX is pink.
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volunteer
HFX is gonna be blue. And then for green
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volunteer
I'm gonna do Ben, so we can see on the chart that we have F of X, OK? So whenever we have like a variable, like a variable is basically just the same thing as like a letter, right? So, um
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[ { "pii_type": "PERSON", "surrogate": "Ben", "start": 13, "end": 16 } ]
volunteer
let's use like the letter, like let's like just take explain this to you. So E of X
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volunteer
it's just like a random number, OK, just like help you out. EFX is just the same thing as saying why, OK? And why is what we're using to define our function.
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volunteer
OK, so why we're basically saying like everything that's equal to Y is the function, OK? So over here we have GFX, which is just another way of saying why, OK? So we're saying GFX is 1/3 of F of X. So can you use like a different color? Can you use the red and can you go to F of X on the graph and put like a little dot...
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student
wait on what
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volunteer
on the F of X.
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volunteer
like in the in the table.
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volunteer
just like next to it or anything.
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volunteer
Yeah, exactly. OK, perfect. So you know where the FX is, right? And
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volunteer
over here, we see that X over here, we see the values for X are next to what we see 6, we see 0, and we see 7, OK?
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volunteer
So these value or negative 6, sorry 6 and 7. These are the values for X. Now for F of X, the values are 18
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volunteer
15, and 24.
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volunteer
So, what we're gonna do is first, we're going to define that G(x) is equal to 1/3 of fx, OK? The second step
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volunteer
1 2nd
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volunteer
I'm trying to figure out a way to explain this like easier for you. OK.
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volunteer
So
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volunteer
an equation of is H X. This means that
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volunteer
to find HFX we need to take the G of X value, make it negative, so multiply it by -1, and then we're going to add 4, OK? So we're saying, see how it's negative, we're gonna make it negative, and then we're gonna add 4, OK?
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volunteer
And then
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volunteer
so that's our second one. This is just like understanding the functions, OK? So we understand for GFX we're taking any value from F of X and we're dividing it by 1/3.
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volunteer
OK? And then we see over here, for H of X,
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volunteer
over here for H of X, we're seeing we're making the, the value for um GFX negative and then we're adding 4 to that value, OK? So our second step is going to be to calculate the GFX values. So we are given F of X values for certain x values. So we can see over here what I'm talking about. For F(x), we see these three va...
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student
yes
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volunteer
OK, that's good. So we see these values for F of X, OK?
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volunteer
So the next thing that we're gonna do,
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volunteer
is
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volunteer
we are going to use the formula for GFX, which is 1/3 of FFX to calculate GFX for each X. That sounds like a lot, but I'm gonna walk you through it. So first, for X equals -6, because do you see how over here we have G and then instead of the X right here, instead of the X, we're replacing it with a -6.
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volunteer
OK, wait, sorry, one second. I just got a call from someone. I will call them back, but, so you see right here, we're gonna do G, and then we're gonna plug in the negative6, and that's going to be the same thing as doing 1/3 times F of -6. So, so to write it down underneath.
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student
ok
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volunteer
Also, I'm gonna do the first one like with you, and then for the second one, I want you to try it on your own. So,
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volunteer
over here
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volunteer
for GFX
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volunteer
we would do G.
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volunteer
times 6
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volunteer
OK, hold on. Let me just erase all of this like Y equals stuff over here.
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volunteer
OK, wait, I don't know why it's not letting me
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volunteer
erase it. OK, let me just erase this right here. OK.
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volunteer
So here we would have GF 6 is equal.
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volunteer
1 2nd. GF 6
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volunteer
OK, I don't know why it's not letting me draw, OK, there we go. Perfect. So we have GF 6 is equal to 1/3, because you see how the 1/3 is in the in the regular formula up here, 1/3 of F of X, so 1/3
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volunteer
of F
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volunteer
of F of X
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volunteer
So 1/3 of F of -6.
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volunteer
because you see how the 6 is at the top right here.
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volunteer
OK, this is just gonna be the same thing.
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volunteer
as 1/3
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volunteer
times -18, which is just going to give us negative 6.
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volunteer
OK. So we're saying here that G of -6 is -6.
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volunteer
OK. So all we're doing is we're taking the value that we're given. I'm gonna do like a complete, I'm gonna do like this teal color. We're taking the value that we're giving.
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volunteer
that we're given, and we're going to put it where the X is, OK?
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volunteer
We're gonna put it where the X is.
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volunteer
and we know that this this um value is gonna be equal to 15.
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volunteer
So
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volunteer
G 0 is going to be equal to 1/3 times F of 0.
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volunteer
And then over here we see F of 0, right? F of 0 is going to be 15.
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volunteer
So I'm gonna do this. I'm gonna give you 5 minutes, um, I'll be right back, because I have to go get my supplies to help you out really quick, but I will be back in just about 5 minutes, and I want you to go ahead and try these next two problems by yourself.
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student
ok
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volunteer
hi
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student
hi
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volunteer
OK hi. So I'm back and let me know if you have any questions or you want me to explain it
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volunteer
cause it's a little confusing. So if you need help, I'm here to help you.
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student
I got 5 and 8
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volunteer
You got 5 and 8.
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volunteer
Yeah.
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volunteer
So for G(0), that is 5 great job and for GF 7 that is 8, so great job you did that right.
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volunteer
So using the same pattern, do you want to go ahead and try H of X? Or do you want me to walk you through it for the first one?
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student
I'll try
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volunteer
OK, perfect. Let me know if you have any questions.
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student
I think I need help
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volunteer
ok no problem!
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volunteer
what part do you need help on
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student
the negative thing
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volunteer
okay give me on sec!
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volunteer
OK. So to approach this, the first thing that we're going to do is
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volunteer
we're gonna fill out the chart for what we already know. So
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volunteer
give me one second. I'm trying to make room
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volunteer
um, for this. OK. So we know the answers for the G values, right? So we know that the answers are gonna be -6
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volunteer
Oh, hold on one second.
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volunteer
We know that the values
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volunteer
I don't know why it's not letting me draw, but
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volunteer
OK, we know that the values are going to be -6.
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volunteer
um 5.
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volunteer
and 8, right? So we know the values for these.
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volunteer
Now, what we're gonna do to find the HVX for H X is that number one, we know the GFX for each value of X, so all we're going to do is we're gonna take the negative of the GFX and add 4. So, for example, if we're looking at age of 6, what we're going to do
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volunteer
is we're going to just take
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volunteer
-6, and we're going to multiply it by
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volunteer
a negative, so basically we're replacing the X over here in the equation. So we're doing negative G of X, right? Our GFX right here, the GFX is just the value we got up here.
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volunteer
So the value we got up here is -6, so we're replacing the GFX with -6, and on the outside of the GFX, do you see how we have a negative sign. So that's why I'm putting a negative sign right here. And then we're going to go ahead and add 4 to this value. So negative times the negative is always going to be a positive, s...
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volunteer
OK?
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volunteer
Then we're gonna have more. So we're gonna have 6 + 4.
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volunteer
And this is gonna go ahead and give us 10.
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volunteer
OK, so that's how we got the number 10. Let me know if you understand. Let me know if you want me to walk you through the next problem. Um, or if you want to try it on your own.
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student
ohhh yes I get it
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volunteer
or if you have like a specific question. OK, perfect. So literally all we're doing is we're replacing the GFX with the value that we got before. So it'd be 6 for GF 65 for G of 0, and um 8 for GF 7. So we're just gonna take those values and replace it of G(x) and then just literally just do it like normal. So yeah, I t...
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