Anyone here real good at Algebra 2 (composition of functions)??
- Thread starter klmno
- Start date
T
TeDo
Guest
Don't quote me 100% but I think it's close if it's not right on. First you have to do g(-a) by substituting -a for the x. The carrot symbol means "raised to the power". This should give you
(-a)^2 +2
= a^2+2.
Then you take that and substitute that back into the original equation again giving you (a^2 +2)^2 +2
= a^4 +4a^2 +4 +2
=a^4 + 4a^2 +6.
Like I said, not 100% positive but pretty darn close.
(-a)^2 +2
= a^2+2.
Then you take that and substitute that back into the original equation again giving you (a^2 +2)^2 +2
= a^4 +4a^2 +4 +2
=a^4 + 4a^2 +6.
Like I said, not 100% positive but pretty darn close.
g(f(a)) means that you first substitute the a into the f function to get 3a - 5. Then you substitute the 3a - 5 into the g function:
x^2 + 2
(3a - 5)^2 +2
(3a - 5)(3a - 5) + 2
9a^2 -15a -15a +25 +2
9a^2 -30a + 27
So g(f(a)) = 9a^2-30a + 27
Here is a great video that might help:
http://patrickjmt.com/composition-of-functions/
www.patrickjmt.com is an awesome site that has videos to help with anything you could want to know about algebra.
x^2 + 2
(3a - 5)^2 +2
(3a - 5)(3a - 5) + 2
9a^2 -15a -15a +25 +2
9a^2 -30a + 27
So g(f(a)) = 9a^2-30a + 27
Here is a great video that might help:
http://patrickjmt.com/composition-of-functions/
www.patrickjmt.com is an awesome site that has videos to help with anything you could want to know about algebra.
T
TeDo
Guest
Way to go Kathy!! That's exactly it klmno. You do the inside function first and then substitute that whole answer for the variable of the "outside" function. Does that make sense????
klmno
Active Member
Yes, that makes sense and for some odd reason, I thought I understood what you said TeDo and Kathy- both- thank you, Ladies! As always, you amaze me with what a person can learn here!
I'm not doing E's homework for him but said I'd put the question here since he doesn't know anyone here to ask outside of school and we live so far out in the country now, his bus is always late to school in the mornings. I don't know if he's too spent tonight to go over this but he can look at it tonight or tomorrow, and also bookmark that link.
Thanks again!!
I'm not doing E's homework for him but said I'd put the question here since he doesn't know anyone here to ask outside of school and we live so far out in the country now, his bus is always late to school in the mornings. I don't know if he's too spent tonight to go over this but he can look at it tonight or tomorrow, and also bookmark that link.
Thanks again!!
Hound dog
Nana's are Beautiful
I'm just sitting here in awe of you all able to do HS math.....................or um, the way it's done now. I have issues helping Darrin with his 2nd grade math for pete's sake.......and from what I've seen they seem to do their utter best to make very simple concepts extremely difficult. ugh
I used to love love love algebra way back in the day, looked forward to going to class......I loathed any other math class except algebra. For some odd reason it just "clicked" with me and I caught on easily. Now? Phht.......lol
I used to love love love algebra way back in the day, looked forward to going to class......I loathed any other math class except algebra. For some odd reason it just "clicked" with me and I caught on easily. Now? Phht.......lol
T
TeDo
Guest
Hound, it helps that I tutored remedial Algebra in college and now have a 21 year old niece and 18 year old nephew that had to do this recently (with a LOT of explanation/tutoring from auntie here) and that I worked in the math dept at the school here. difficult child 2 finished Algebra 1 this spring and difficult child 1 is starting it next week. It's a good thing I DO know how to do it or all 4 of these kids would have been doomed.
T
TeDo
Guest
I didn't just "remember" it. I had to read their book to remind me how to do it and/or learn how to do it again. It took some time but now I'm just an old hand at it. It really does require a whole different level of thinking. We'll see how soon I forget it again once both of mine are through Algebra 2. LOL
klmno
Active Member
There were times when I was in school and also when I was trying to help E with homeowrk that I couldn't even decipher the instructions from the teacher but if I looked at the problem and figured it out or had it explained to me a different way, or explained it to E a different way, it seemed much easier and I "got it" and learned the concept. I don't know if that means we have a learning disability, we just think differently than most people, or if we are intellectually limited. Or if teachers are typically teaching to one personality type or learning group. I (and E) have gone from clueless to completely understanding just due to a concept being presented differently.
E and I both remembered (this evening) a few times when he was in middle school when he showed me "difficult" homework, I read the instructions, and said WTH!! Then after reviewing the book, I said "this is easy", told him what I could see was being done and asked for, and then he said "oh, no problem- I can do that". Is that a difference in teaching methods or learning styles or IQ????
E and I both remembered (this evening) a few times when he was in middle school when he showed me "difficult" homework, I read the instructions, and said WTH!! Then after reviewing the book, I said "this is easy", told him what I could see was being done and asked for, and then he said "oh, no problem- I can do that". Is that a difference in teaching methods or learning styles or IQ????
DammitJanet
Well-Known Member
I think its a different way of learning and doing. See..I come from the dark ages where if you used a calculator to do algebra it was cheating. Now they want you to buy these expensive things and learn to do algebra on them. I think I somewhat understood what Kathy was saying but it made no sense to me because it sounded like more steps. F function? Huh? Why dont I just solve 3e + 5 = 27. (Just using that for example) Please dont actually make me do math because I have lost that ability with the meningitis.
But to me it seems much better to learn the concepts of x + y= z than to enter it into a function button and then into a G button.
Of course I also believe in teaching kids the times tables too.
But to me it seems much better to learn the concepts of x + y= z than to enter it into a function button and then into a G button.
Of course I also believe in teaching kids the times tables too.
T
TeDo
Guest
difficult child 1 is one of those that needs explained in much different ways but then he IS on the spectrum. Textbooks are typically written to the neurotypical thinking skills of the average student. Then they present this same information/textbook to a kid on the spectrum or who has a learning disability (math, reading, doesn't matter) who is perfectly capable of understanding it if it was explained in basic and simple language. difficult child 1 is better at analyzing examples than having it explained OR from reading the book himself. It's just a different thought pattern/learning style.
Hound dog
Nana's are Beautiful
Janet, I also come from those dark ages. lol And soon as they start giving instructions for doing the problems with the calculator.......I'm totally lost. I think they're cheating the kids to teach them to do the math that way at the very beginning. We're teaching them to be overly reliant on gadgets to do the real work for them and to not really think about it all the way through.
When mine were young, they weren't allowed a calculator for homework (I didn't give a darn what the teacher did/didn't want) and I refused to buy them one for class. I don't think they even saw one until college.....unless the teacher had some in the classroom.
I watched in my college algebra course grown people reduced to tears because using the calculator only made it ten times more confusing. (didn't help they didn't know how to use the calculator properly either.......which included me) Bff and I had to tutor classmates on the steps worked out on paper (heaven help you if you tried to follow professor skip ten steps) .......and bff tutored all of us on wth the buttons on the calculator did. Not that teaching me a calculator did much good. If I tried to use it I couldn't work the problem. Since the professor had problems worded such you had to use it......well, there is a reason I barely passed the course and it wasn't all Traumatic Brain Injury (TBI) related. (or I don't think it was as I wasn't the only one having issues.)
I'm weird. I learned math pre kindergarden as money. I learned to add/subtract/ and figure in tax percentage before I ever went to school. So, if I'm dealing with numbers........I think in money. (which is why I caught on to the metric system and decimals so easily) There is one hitch to this "talent" or having learned this way. Standing in a store you don't have pencil and paper, not that I could write anyway at the time. lol I got into more trouble for not being able to show my work than anything else in school. I couldn't show my work because it was in my head, and it was automatic.......and I just "knew" the answer. How I got the answer I couldn't explain because I learned to do it so young that honestly, I dunno how I did it........or do it now when it decides to work properly. When I tried to show my work......I usually got the answer wrong because I'd manage to mix myself up. The only thing I could show my work on was algebra.....because of this cool thing the teacher did making a pattern out of the problem that was a smilie face......and I'm weird and liked making the smilie face. lol
My poor grandma was just trying to teach me how to manage money, I'm sure she didn't mean to mess me up with math. Fractions nearly gave me a nervous breakdown until we got to the part where they become decimals then I was like Ohhhh money!
But I'm still not that hot with fractions, even worse now after the accident.
Darrin was doing double digit math last year but the problems were set up like this: 24 + 36 = ___ and he was expected to work them that way. He couldn't figure it properly to save his life. So easy child showed him how to line them up and then add them complete with carrying the number over when needed. It took her a long time because that is sooooooooo not the way they're teaching it, they've got some weird method that is so around the barn neither easy child (who is excellent at math) nor I can figure out what the point is. He is lucky, his teacher didn't mind easy child showing him the "old" way to do it. But I've had teachers have a major fit and give my kids an F for stuff like that.
When mine were young, they weren't allowed a calculator for homework (I didn't give a darn what the teacher did/didn't want) and I refused to buy them one for class. I don't think they even saw one until college.....unless the teacher had some in the classroom.
I watched in my college algebra course grown people reduced to tears because using the calculator only made it ten times more confusing. (didn't help they didn't know how to use the calculator properly either.......which included me) Bff and I had to tutor classmates on the steps worked out on paper (heaven help you if you tried to follow professor skip ten steps) .......and bff tutored all of us on wth the buttons on the calculator did. Not that teaching me a calculator did much good. If I tried to use it I couldn't work the problem. Since the professor had problems worded such you had to use it......well, there is a reason I barely passed the course and it wasn't all Traumatic Brain Injury (TBI) related. (or I don't think it was as I wasn't the only one having issues.)
I'm weird. I learned math pre kindergarden as money. I learned to add/subtract/ and figure in tax percentage before I ever went to school. So, if I'm dealing with numbers........I think in money. (which is why I caught on to the metric system and decimals so easily) There is one hitch to this "talent" or having learned this way. Standing in a store you don't have pencil and paper, not that I could write anyway at the time. lol I got into more trouble for not being able to show my work than anything else in school. I couldn't show my work because it was in my head, and it was automatic.......and I just "knew" the answer. How I got the answer I couldn't explain because I learned to do it so young that honestly, I dunno how I did it........or do it now when it decides to work properly. When I tried to show my work......I usually got the answer wrong because I'd manage to mix myself up. The only thing I could show my work on was algebra.....because of this cool thing the teacher did making a pattern out of the problem that was a smilie face......and I'm weird and liked making the smilie face. lol
My poor grandma was just trying to teach me how to manage money, I'm sure she didn't mean to mess me up with math. Fractions nearly gave me a nervous breakdown until we got to the part where they become decimals then I was like Ohhhh money!
But I'm still not that hot with fractions, even worse now after the accident.Darrin was doing double digit math last year but the problems were set up like this: 24 + 36 = ___ and he was expected to work them that way. He couldn't figure it properly to save his life. So easy child showed him how to line them up and then add them complete with carrying the number over when needed. It took her a long time because that is sooooooooo not the way they're teaching it, they've got some weird method that is so around the barn neither easy child (who is excellent at math) nor I can figure out what the point is. He is lucky, his teacher didn't mind easy child showing him the "old" way to do it. But I've had teachers have a major fit and give my kids an F for stuff like that.
Lisa, Lisa... I'm having serious flashbacks. In reverse.
difficult child absolutely insisted he could not possibly do fractions. We didn't eat pizza and pie, and he couldn't relate to the examples they were using. No clue at ALL. Until one year the teacher in desperation brought up the issue... and all I did was turn to difficult child and start listing off construction measurments. What's three and three eights plus 4 and a sixteenth? And he knew the answer, but insisted those weren't fractions, they were measurements! Took a bit to broaden his scope, to teach him to generalize, because he was only used to the power-of-two fractions - half, quarter, eighth and so on - the ones you find on... a construction tape measure. After that, he caught on to decimals too, based on it being "money"... but only to two decimal places, because you can't have half a cent...
DammitJanet
Well-Known Member
Cory can do fractions in a snap because of construction. The boy has a 9th grade education....actually he barely spent anytime in a regular classroom past 5th grade. After that he was in a wilderness camp for all of 6th grade, half of 7th then in a self contained emotionally disturbed class from the second half of 7th until he quit school in 9th. In those classes they only had worksheets and no actual teaching. It was a holding pen. I think he went to at least 7 different schools between those years. He quit school at 15.
AnnieO
Shooting from the Hip
in my opinion, having to get a calculator for a 4th grader (which we had to do) IS cheating the kid. Heck, I didn't even have one for college math.
...._12_
10 | 120
....-10_
......20
.....-20
.......0
But her teacher gave her an "F" because clearly I did the work.
Onyxx had problems with division, so I showed her "long division":
...._12_
10 | 120
....-10_
......20
.....-20
.......0
But her teacher gave her an "F" because clearly I did the work.
I must be a really "bad" teacher; I still show my students long division the way Step does and adding the way Lisa does! Also my 5th graders are not allowed to use calculators (except once in a great while). Doesn't mean I don't show other ways as well but I figure (no pun intended
) that I need to reach students in whatever way I can.
) that I need to reach students in whatever way I can.
Hound dog
Nana's are Beautiful
No, wiped out, you're an excellent teacher and your students are getting a real education they can understand and will carry them through their lives.
I had college professors who couldn't for the life of them figure out what was wrong with my children's generation that they couldn't do normal equations, most especially without calculators. Obviously, they'd never tried to help their child with homework. The younger the kids got, the worse the problem got. Spelling is no better. Here in younger grades they're encouraged to spell phonetically.....and are not marked wrong if they've done it that way on anything except the spelling list. This is carried out throughout high school. So now, as well as kids who can't do simple math, you have a vast number of kid who have no idea how to spell correctly even some of the simplest words. Nichole had a hard enough time with the dyslexia.......but add in the phonetic spelling junk, and she still has a hard time spelling words correctly. (although now she'll look them up for correct spelling)
Old methods worked and produced people like Einstein. Now granted, some kids have trouble with that method.....but like you Sharon, most good teachers can find an alternate way to help them learn. All this changing curriculum every time they turn around is confusing to the kids, and has got to be a nightmare for teachers to keep up with. And then you have those teachers just teaching for the proficiency tests......and I won't go near my soap box on that one.
I had college professors who couldn't for the life of them figure out what was wrong with my children's generation that they couldn't do normal equations, most especially without calculators. Obviously, they'd never tried to help their child with homework. The younger the kids got, the worse the problem got. Spelling is no better. Here in younger grades they're encouraged to spell phonetically.....and are not marked wrong if they've done it that way on anything except the spelling list. This is carried out throughout high school. So now, as well as kids who can't do simple math, you have a vast number of kid who have no idea how to spell correctly even some of the simplest words. Nichole had a hard enough time with the dyslexia.......but add in the phonetic spelling junk, and she still has a hard time spelling words correctly. (although now she'll look them up for correct spelling)
Old methods worked and produced people like Einstein. Now granted, some kids have trouble with that method.....but like you Sharon, most good teachers can find an alternate way to help them learn. All this changing curriculum every time they turn around is confusing to the kids, and has got to be a nightmare for teachers to keep up with. And then you have those teachers just teaching for the proficiency tests......and I won't go near my soap box on that one.
