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NationalTutoringObservatory
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MathEd-PII

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volunteer
sorry 3 root n
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student
Oohh, so the range in the function is defined by the domain, if n can't be negative and has to be greater than or equal to 0, m has to be the same, right?
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volunteer
Well, that changes on the function. The domain is not always equal to the range. Imagine a vertical shift up 1 for this same function. The domain would be the same but the range would be [1, infinite)
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student
So it depends on the starting point basically, so if it was n≥4, it would start at four and be [4,∞)
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volunteer
That is 4 the domain. The range would still be [0, infinite). What I am talking about with a vertical shift is a +1. See graph :)
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volunteer
You are right about that being the domain. The range is altered by a different value though.
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volunteer
Your problem does not have a vertical shift. So don't worry too much about it for this particular question.
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student
So it would shift up depending on the y function, so if it m=3√n+4 it would still start at 4
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volunteer
The range would start at 4, yes.
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volunteer
The domain is still [0, infite)
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student
So the range for this function would be m≥0 because it starts at 0 and continues that or [0,∞)
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volunteer
Yes. That is right!
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volunteer
Do you understand it well enough?
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student
Im getting there, if I were to see it on a test I would freeze
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volunteer
Yes. You can always just use the graph. There are only a few you will ever see in Algebra 2. You have to use the original function and apply the transformation sto get the domain and range.
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volunteer
This is radical. I will put a few on the bottom of the current graph.
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volunteer
Have you seen these?
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student
I think I have but I can't be too sure
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volunteer
Okay. It is the start of the school year, so you will.
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volunteer
Just remember that this question already gave you the input (n, often seen as x)
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student
I'm in Algebra 2 algebra, so we kind of go through topics very fast, it doesn't help that I missed this topic in algebra 1
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volunteer
You already had the domain/
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volunteer
Okay. I also skipped Algebra 1. Khan Academy. It truly explains everything very well. Algebra 2 does become much easirer with a lot of Algebra 1 practice.
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student
That's what I've heard, I'll make sure to stay on top of that!
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volunteer
Yes. It is great. Remmember to keep inputs and outputs straight and to always look for what the problem already gives you.
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volunteer
x and y are not the only possible function variables.
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student
Question, if f(x)=x⁴ and domain is xeR, all real numbers would the range be all real numbers to?
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volunteer
For this question, I believe so.
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volunteer
The root is even so all numbers will be positive. The lowest (x=0) will be negative.
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volunteer
Great job!
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volunteer
sorry x=0 will be 0
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volunteer
NOT negative
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student
And for this question I'm going to write it out
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volunteer
You can write it out if that helps you. :)
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volunteer
Okay. This is absolute value.
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volunteer
The range is [0, infinite) and the domain is all real numbers (here, the horizontal shift does not matter)
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student
How did you get that
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volunteer
Do you see the graph?
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student
Yes
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volunteer
What are all the possible x-vales?
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volunteer
values
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volunteer
Over what portion of the x-axis will it cover?
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student
Anything between -10 and 10
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volunteer
Why do you think that?
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student
Wait, anything less than or equal to -10 and 10 because of the symbol
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volunteer
No. It is all real numbers because it stretches infintely on the x-axis in both directions.
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student
How?
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volunteer
The graph is a V and its sides are contining forever (per the nature of the graph). The arrows represent infinite.
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student
But wouldn't it be negative
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volunteer
all real numbers includes possible negative values
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student
So what does the domain indicate
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volunteer
the x-values that can be inputed
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volunteer
the range is separate on the y-axis
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volunteer
Liam, I am so sorry but I must leave the session. You have been great. Contact support or requesting another session to continue your learning.
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[ { "pii_type": "PERSON", "surrogate": "Liam", "start": 0, "end": 4 } ]
student
Thank you again for all your help
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volunteer
Your welcome!
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volunteer
hello
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student
hiii
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student
ow r uu
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volunteer
good
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volunteer
how can i help you today
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student
I need help preparing for a unit exam
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volunteer
did you want me to walk you through solving this problem?
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student
yes that would be great
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volunteer
alright sounds good
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volunteer
so do you know what complementary means
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student
yes but I forgot
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volunteer
alright so complementary angles are angles whos sums add up to 90 degrees
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student
ok thats what I thought
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volunteer
so we know that these two angles that we have to solve for add up to 90
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student
ok
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volunteer
so then it says one angle is 3 degrees less than 2 times the other angle
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volunteer
which i wrote as x=2y-3
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volunteer
so now that we have that we can plug 2y-3 in for x
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student
ok that makes sense
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volunteer
so when i plug that in i get 31 =y
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volunteer
or 31 degrees for angle 2
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student
ok
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volunteer
however the question is asking for both angles
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volunteer
so we can plug in the value we got for y
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volunteer
to find x
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volunteer
and we get x=59
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volunteer
any questions
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student
nope
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volunteer
alright sounds good
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volunteer
anything else you need help on today
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student
no thank u so much that helped a lot
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volunteer
k
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volunteer
well good luck on your exam
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volunteer
and have a great rest of your day
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student
u too
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student
Hello I need help with solving this I honestly don't understand it since this has no numbers
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volunteer
ok
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volunteer
basically it just wants you to get b on one side of the equal sign by itself
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student
yeah ik but like how
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volunteer
so
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volunteer
if we want to isolate b
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volunteer
what should we remove first from the left side
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student
b?
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volunteer
We want to remove all other terms from the left side so that we can solve for b(isolate b)
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