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ChrisB

Transformations of Functions

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This is DD15's first year at our local Catholic HS as a sophomore.  In her Adv. Algebra II class, transformations to functions are being introduced (Pearson text-Common Core), and she's having a hard time understanding this concept, maybe because she's new to functions in general.   Is the first month into an advanced algebra II class a normal time to see transformations?  I understand sequences are different between curriculum, but it seems early for it.  

She came to me last night upset that she had no clue what was going on in the unit.  I was able to talk her down and figure it out with her, although, I don't remember these from back-in-the-day.  For reference, last year we covered over half of AoPS's Intro to Algebra and Jurgensen's Geometry, going through basic quadratics (we never made it to graphing quadratics). 

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When I look at math now, I have memories of slogging through it the hard way, and barely understanding it conceptually.  The tools that are available now make it so much more transparent.  I just went and looked up Transformations on Purplemath and found a great article.  And then if I wanted to, I could put some functions into Desmos and play around with some transformations, and see the new graphs right away.  I never had that so easily available.   I had to make an appointment at the math lab on campus and have a computer reserved as well.  Everything is right there for everyone now.  So cool.  

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Functions are really hard to wrap your head around.  Even AoPS covers functions in 2 different textbooks: Intermediate Algebra and Precalculus.  Even the discussion of shifting functions left/right, up/down, stretching/shrinking, and reflecting is presented twice in AoPS because it can be counter-intuitive.   

Is she stuck on the fact that y = f(x + k) is a leftward shift of the graph y = f(x)?  She may need to work through some problems slowly to see why this is the case.  

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I think she has the basic idea now after our "transformation throwdown"😉 (working through several problems slowly) , but I was curious if it's early to see them in algebra.   Kinda like introducing functions and quickly talk transformations vs. talk functions, and then after developed understanding, drill down to transformations.  Maybe I'm misunderstanding transformations and the curriculum, but that's what it seemed to me.  Like giving the cheat-sheet before better function understanding...I don't know. 

All that to say, I posted because it seems out of place to me and wondered if it was me or the curriculum...lol  

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The Algebra 2 book I'm using is Holt from 2007, and transformations are throughout the book. The first chapter has an introduction to functions and transformations. Then as each type of function is taught, the transformations are revisited in more detail. 

The lessons have really good free videos online, so you might want to get the book and could line up her lessons with the book's lessons. 

 

Edited by mom31257
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This is something people generally have tons of trouble with, especially the horizontal shifts. I recommend graphing quite a few transformations by hand, mostly with graphs of functions without a formula, so you can really see how the points are changing.

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On 9/24/2019 at 8:17 PM, daijobu said:

Is she stuck on the fact that y = f(x + k) is a leftward shift of the graph y = f(x)?  She may need to work through some problems slowly to see why this is the case.  

I agree that working out some problems will help her see that. As I'm tutoring students, I stress that when a subtraction sign is in a formula, a negative number will change it to a plus. They already know this, but it's challenging to identify it. I try to teach them that anytime there is a plus sign in those type of equations, they know that it was actually a negative number there originally. When I introduce each new formula (i.e. distance formula, point-slope formula, transformations, etc.), I write it out using one color for all the permanent parts and different colors for the numbers that change with each situation. 

Edited by mom31257
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I gave her your suggestion of using different colors since she likes multi-colored organization.  She's almost through the chapter now and has a section quiz on Monday and chapter test later in the week.  Just with the practice between when she came to me all concerned and now, she's gained much more confidence with transformations.  So, we'll see...

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