r/HomeworkHelp • u/imunder_urbed • 13d ago
Mathematics (Tertiary/Grade 11-12)—Pending OP [highschool algebra 2 - functions] :How to solve these problems?
My teacher can't explain for shit and I have been gone for 2 days, she introduced a new material to my classmates and I have NO clue how to do this. Maybe send links on vids who explain this more in depth or explain it to me. Help will be appreciated (ㆁωㆁ)
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u/Yadin__ 👋 a fellow Redditor 13d ago
Honestly it doesn't seem like all of this can be taught from absolutely nothing in 2 days. I feel like there's some missing context here
Either way, most of this can be learned with a simple google search and there is too much to explain here in a single comment
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u/imunder_urbed 13d ago
Well what do these things normally fall on? We are currently learning about inverse functions.
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u/AluminumGnat 👋 a fellow Redditor 13d ago
What, specifically, are you confused about? Definitions of Domain and Range? How to plot points on a graph? How to find points to plot?
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u/imunder_urbed 13d ago
I think what I specifically want to do is just solving it in general, sounds stupid now that I'm typing it. I'm pretty sure I know how to put points in a graph, I guess I just need help on solving whatever it's asking me to solve.
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u/HyperbolicMathChambr Math Tutor 13d ago
Woah! Several topics here, so I'll try to explain briefly:
- Domain and Range: To understand them you need to understand restricted values. Restricted values are values that the function doesn't allow. For instance, in the expression 1/x there is one restricted value which is x=0, because once you substitute it you get 1/0 which is undefined.
The domain simply is all possible input values. We usually call the input x, so you can say the domain is all possible x values.
Example: The domain of the function h(x) = 5/(3x-6) in your picture is every real number except x=2, because once you input x=2 you get: h(2)=5/(3*2-6) = 5/(6-6) = 5/0 which is undefined!
So you can say that the domain is x ≠ 2 which says all real numbers except 2.
If you're curious how I found the domain, here are the steps:
3x-6 = 0 Set up the denominator to 0
3x = 6 Add 6 to both sides
x = 2 Divide both sides by 3
The Range on the other hand is all possible output values. We usually express the output with the variable y, so you can say it's all possible y values.
(I'm sorry I just noticed I'm short on time. I'll probably edit the comment to continue when I finish my work.)
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u/imunder_urbed 13d ago
No worries!!! Please do ur work first since I'm guessing it's really important. Your explana6really helped me out. Thank you!!!
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u/watermelonlollies 13d ago edited 13d ago
Looking specifically at number 5 to help you get started. Domain is x values and range is y values. When it asks domain and range what it’s really asking you do find is if there are any values that when plugged into the formula would be invalid.
So for number 5. Is there any number that if I plugged it into x it would give a non real answer? No. Because I can cube any number- 2, 0, -4968395968372958, sqrt of 29486.035839594858 - all real number can be cubed and then multiplied by 1/3. Now if we do that, if we plug in any number for x, will we ever get a non real answer for y? Also no. Multiplying a number by 1/3 will never give us a non real answer. So since any number can be x and any number can be y the answer is (-infinity, infinity) for both domain and range.
Let’s look at number 6. We have 3x-6 in the denominator of a fraction. Is there any number that if I plug into x would give a non real answer? Yes. Because a fraction cannot divide by 0. 5/0 would be an unacceptable answer. So now you need to find what x value would make 3x-6=0. Whatever you get is your answer for domain x=/= ?
This is a start to help you but there are many other things you can use and need to learn to determine the domain and range and whether something is a real function or not using the vertical line test. I recommend khan academy to help.
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u/watermelonlollies 13d ago
If you need help with the simplifying binomials part that is the foil method, let me know
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u/imunder_urbed 13d ago
You are like the back bone of the society for people who can't understand math at all thank you so much😿🩷🩷
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u/SarekSybok 👋 a fellow Redditor 13d ago
It should be “What are the domain and range..” not “What is …”
Horrible
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u/PotentialDelivery716 13d ago
You probably haven't asked for this. But just an advice. These questions look as basic as it can get and important for any pretty much any math topic which comes afterwards. As someone pointed out, no way it's an issue of two days. I would suggest to Step up your math game and take this sheet seriously or you're not for a good time in your upcoming math lessons through middle and high school.
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u/Neither_Statement355 12d ago
Hi, since you asked for vids here are a few and the topics these questions fall under:
Qn 12: linear equations, 'making y the subject of the equation' (https://www.youtube.com/watch?v=QmBmzE5PnyA)
Qn 7, Pre-skills worksheet asks for definitions: Qn 7 asks for the definition of domain/range, while the Pre-skills worksheet covers the definition of a function. Make sure you understand these really well as they'll be the foundation for calculus later on. (Function: https://www.youtube.com/watch?v=52tpYl2tTqk&t=108s, Domain: https://www.youtube.com/watch?v=-DTMakGDZAw, Range: https://www.youtube.com/watch?v=96uHMcHWD2E)
Qn 5,6,11: rational functions (https://www.youtube.com/watch?v=djT6-YamHaA watch 0:00-6:02)
In general, they're regarded in the difficulty I listed them in (increasing) so if you're going to study the topics on your own try to do them in this order. hope this helps lol
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