Jacobs Algebra question

[Heather in AL]

Hi everyone,

 

I mistakenly posted this on the general forum, so I thought I should ask here.

 

I switched my dd to Jacobs Algebra after completing Saxon Algebra 1/2. She has finished chapter one and we have already hit a snag in chapter two.

 

Chapter two, lesson one introduces functions. They basically tell the student to "make a guess" as to the function (according to the TM). In Set II, problem 6 i and 6 j the functions aren't obvious just by looking. In fact, 6 j is one that I couldn't figure out and had to ask hubby.

 

Has anyone else had this problem, or is it just me/us? Hubby is very mathy and tried to explain it, but he used terms that dd hadn't had yet like linear functions and quadratic functions.

 

Is there something we should have done before jumping from Saxon to Jacobs?

 

Help!

Edited November 2, 2009 by Heather in AL
Because the post posted w/o my knowledge before I was finished! :-)

[Greensa]

Just to be sure whether we have the same edition of Jacobs... Is the answer to 6i. y=12-x and the answer to 6j. y=20/x? If so, no, it's not obvious but can be guessed (with the help of lots of paper and stubbornness:tongue_smilie:).

 

About the concern it generates... my feeling with the book is that Jacobs wants the student to try to figure things out on their own without a detailed explanation before he gives that detailed explanation. He has explained everything so far clearly enough that my decidedly non-"mathy" daughter understands it, but does tend to toss things out there to look at before providing the explanation.

 

We didn't use Saxon so I can't say for sure, but from what I have seen of it when choosing programs, that seems to be very different from Saxon's approach. I'd say keep trying. You may like his approach once you adjust. My daughter does. She says that it's a lot closer to fun than any other books she's seen.:)

 

Sara

[MyThreeSons]

When trying to figure out the function, given several pairs of numbers, here are some things to do. Start by looking at the progression of y values.

 

1) If they increase (or decrease) by a constant number, use that constant value as the multiplier for the x value, and then see what adjustment you need to make to get to the proper y value. So, #6f, the y values go up by 6 each time. Multiply each x value by 6, and you see that you then need to subtract 1 to get the correct y value, so the answer is 6x - 1. On #6i, note that the y values decrease by 1 each time, so you want to multiply x by (-1), then make your adjustment: y = -x + 12.

 

2) If the y values change by different amounts each time, think about squares or cubes. For #6e, notice that y jumps by a bigger number each time, but not much bigger, so think about squares. If you square each x value, you'll see that you need to add 1 to get y, so the answer is y = x^2 + 1.

 

3) On something like #6j, where you see an irregular progression of y values, try looking at the relationship between the x and y values directly, first using one of the basic math functions. In this case, you should see that in each case, x times y = 20. All you have to do is rearrange the equation to get y = 20/x. This technique would also work with #6i, where you see that the x and y pairs always sum to 12, so the function is y = -x + 12.

 

4) For more complicated functions, where the above techniques don't yield results, I find it helpful to write out new rows, such as x^2, x^3, 2x, etc, and apply the above techniques to combinations of those rows.

 

5) Beyond this lesson (and for solving these types of problems in general), you can also try making a graph of the function, using the x-y pairs. As you become more familiar with the properties of graphs, you can sometimes figure out what the function is by looking at the graph.

 

HTH

[EKS]

That's the idea, if I remember the lesson correctly, that making a "guess" is easy sometimes but other times it isn't.

 

For the ones she couldn't get, just tell her the answer, show her how is works, and move on.

 

You will see more of these types of problems occasionally. She'll get better at solving them as she learns more about various types of functions. But occasionally my son couldn't get them either and it was fine.

 

A lot of the ones my son couldn't get were of variations of these two types:

 

y=a/x and y=a-x.

Edited November 3, 2009 by EKS

[Heather in AL]

Thanks so much ladies! Dh is satisfied now that he knows we didn't 'mess up' by switching programs. We are having our daughter graph her functions so she can learn to recognize the common ones, and we're taking it all in stride.

 

I don't know which edition we have (I just got it from Rainbow Resource), but it sounds like the editions are the same at this point. Hopefully, dd will become comfortable with this type of problem as time goes on.

 

Thanks again for all the help!!