Expert: Paul Klarreich - 5/10/2007

Question
actually i have a question and two examples. question:  What is the strategy for complicated function rules? I am in the sixth grade taking seventh grade math and i really don't understand how to do this. examples:  the numbers on the left are
0 1 2 3    on the right are
4 3 2 1.        
next example:   the numbers on the left are
0 1 2 3         on the right are
1 4 7 10.  

Answer
Questioner:   Tatyana
Category:  Advanced Math
 
Subject:  function rules
Question:  actually i have a question and two examples. question:  What is the strategy for complicated function rules? I am in the sixth grade taking seventh grade math and i really don't understand how to do this. examples:  

the numbers on the left are  0 1 2 3    
          on the right are  4 3 2 1.        
next example:   
the numbers on the left are  0 1 2 3         
          on the right are  1 4 7 10.
..............................
Hi, Tatyana,

You are lucky that the examples here involve Linear functions -- they will have straight line graphs and will have equations in the form:

y = ax + b  

Note this vocabulary:  

A 'form' is a pattern that is matched by many examples.  For example, the

'form'

y = ax + b

is matched by all of these:

y = 3x + 7,  with  a = 3,  b = 7
y = -2x + 1, with  a = -1, b = 1
y = x - 2,   with  a = 1, b = -2
y = -x,      with  a = -1,  b = 0.

So all you really have to do is figure out which match to use for the

example.  For these 'linear' functions, you have these clues:

****** I have reformatted your numbers. **********
****** Use the Courier Font to view this *********


The 'a', which you must find, is the change in y-values that you get when x

increases by 1 unit.  It can be positive or negative.

In your first example,

the numbers on the left are  0 1 2 3    << x-values.
          on the right are  4 3 2 1.   << y-values.

x changes from 0 to 1 (that's one unit) and y changes from 4 to 3, a

decrease (negative) of 1.  
The same thing happens when  x changes from 1 to 2, and 2 to 3.  IF IT DID NOT, THE FUNCTION WOULD NOT BE LINEAR and things would be much harder.

So you will conclude that  a = -1.  Of course, this has a name.  It is called the slope.

The 'b', which you must find, is the value of y that corresponds to x = 0.  

In this example, it is 4.

You are ready.  Your example is:

y = -1x + 4,  also writable as  y = -x + 4

..............................

In the second example,

the numbers on the left are  0 1 2 3    << x-values
          on the right are  1 4 7 10.  << y-values.

x changes from 0 to 1 (that's one unit) and y changes from 1 to 4, an

increase (positive) of 3.  Conclusion:  a = 3.
The same thing happens when  x changes from 1 to 2, and 2 to 3.  IF IT DID NOT, ... Oh, I said that already.

When  x = 0,  y = 1,  so conclude  b = 1

Function is:  y = 3x + 1

Note: sometimes the function is written with  f(x) [or any other suitable letter] instead of  y.  It's the same thing.

I am sure you will see some functions that are non-linear and have more complicated rules.  It will take you about  110 years to learn them all.  In other words, it's the job of a lifetime.   Have fun!