Function Tables

[johninbigd]

I'm trying to help my girlfriend's daughter with her homework and she's working on function tables. The idea is to view a table of inputs and outputs and figure out what equation or function would produce that result. So far, they've been pretty easy for me and, after some instruction, she's doing a great job with them. Most of them result in something like y=3x+4 or y=x/9 + 2, or something like that. Pretty linear.

Now, we come to a harder one that is really bugging me. I know the solution is "on the tip of my tongue", but it's eluding me. Here is the table:

Input Output
36 9
72 9
24 1
18 0

The part that's freaking me out is that the output for both 36 and 72 is 9. It's also notable to me that the output starts out pretty low (0,1) and then jumps up to 9. An increase in output from 0 to 1 is caused by an increase in input from 18 to 24. But then an input of 36, just 12 more than 24, results in an output 9 times higher than the previous entry.

The function is supposed to be two variables using only multiplication, division, addition and subtraction.

Any help?

Thanks!

 

[Denis]

Are you sure there's no typo...like could the "72" be "30" ?

 

[johninbigd]

Are you sure there's no typo...like could the "72" be "30" ?

It might be a typo on the homework sheet, but that is the table they gave. She is turning it in today, so this won't help her out immediately. But it was really bothering me that I couldn't figure it out! I used to be pretty good at math, but I haven't had to think like that in 20 years.

I'll have to ponder this some more. I'll try to see if I can figure it out if the 72 were actually 30. It still throws me that the values for 30 and 36 as inputs would lead to the same number. The outputs 0,1,9 and 9 seem pretty non-linear. How do you get that non-linear with just multiplication, division, addition and subtraction? Or is that still linear and I just am thinking about it the wrong way?

Thanks!

 

[johninbigd]

As a side-note, what's even more frustrating for me is that her math class doesn't have a text book! They have a workbook with problems, but they're expected to be in class and take notes. If they miss a class, they just have to hope that the teacher has printed notes available. It drives me nuts when I'm helping her with her math and I want to refer back to a textbook but she doesn't have one. Grrrrr!

In this particular case, she missed class the day this was allegedly discussed. And the day the homework was assigned, they had a substitute teacher who apparently didn't have any notes from that day available. So, without a textbook, she's just expected to know how to do the homework. It makes me furious to see math taught this way.

It gets better. On this assignment, she swears that the teacher isn't going to grade them on accuracy. The teacher just wants to see that they did the homework, but supposedly doesn't care about whether or not the answer are right. On some questions, this girl just asked me if she should make a guess since she'll get credit for having something there even if it isn't right. I said that it does no good to guess. This is math. Your answers are either right or wrong and it doesn't make any sense to put down an answer that you can show is wrong in just a few seconds.

Okay, my rant is over. Back to your regularly scheduled program.

 

[Deleted member 4993]

I'm trying to help my girlfriend's daughter with her homework and she's working on function tables. The idea is to view a table of inputs and outputs and figure out what equation or function would produce that result. So far, they've been pretty easy for me and, after some instruction, she's doing a great job with them. Most of them result in something like y=3x+4 or y=x/9 + 2, or something like that. Pretty linear.

Now, we come to a harder one that is really bugging me. I know the solution is "on the tip of my tongue", but it's eluding me. Here is the table:

Input Output
36 9
72 9
24 1
18 0

In the absence of any other information, I can write this as two part function

y = x/6 - 3 ...........for 18 ? x ? 24 [edit]

y = 9 ...................for x > 24

This meets all the stated constraints - it is a function and use only addition, subtraction, multiplication and division.

The part that's freaking me out is that the output for both 36 and 72 is 9. It's also notable to me that the output starts out pretty low (0,1) and then jumps up to 9. An increase in output from 0 to 1 is caused by an increase in input from 18 to 24. But then an input of 36, just 12 more than 24, results in an output 9 times higher than the previous entry.

The function is supposed to be two variables using only multiplication, division, addition and subtraction.

Any help?

Thanks!

 

[johninbigd]

I guess I'll assume that either there was more to the assignment than what was written on the page I saw, or that there was a typo on the page.

Thanks for your help!

 

[Denis]

Picking up on Sir Khan's brainwave:

18/6 - 3 = 0
24/6 - 3 = 1
36/6 + 3 = 9 : 36/6 - 3 = 3 ; betya a buck the 9 is a typo, should be 3
72/6 - 3 = 9

 

[Denis]

I used to be pretty good at math, but I haven't had to think like that in 20 years.

Quit complaining, Big John: twas 40 years for me when I got back to it 7 years ago :wink:

 

[johninbigd]

I used to be pretty good at math, but I haven't had to think like that in 20 years.

Quit complaining, Big John: twas 40 years for me when I got back to it 7 years ago :wink:

Thanks for the encouragement! I was really good at it back when I did it, but I've forgotten most of what I knew back then. I wonder if I can find some online refresher courses for free. lol