Melody

It didn't help me either.  It is good that you had a go LagTho  but i think there are errors in your logic.

Hi Cerenity,

Yes i understand this may not be trivial for you but

Can you answer Rom's question please.

What is f(-2)?  what is g(-2)?

g(x) is in the table of values.  Can you see what g(-2) is?

\(f(x)=3-x^2\)

To find f(-2)  you have to replace the x with -2.   Can you do that for us please. 

You will be more likely to get it right if you put the -2 in brackets like this  (-2)

F(9)=14        look at the table to see what I mean.

You have x on the first row and (x) on the second row.

When x=9 you look underneath the 9 to get the f(9) value.  It is 14.

Now you can tell me what f(5) is.    

The notation is always confusing  LOL   

How did you get your answer?   How far did they each travel and why do you think so.

To other answerers:

Please let Cerentie answer before adding another post.

Your question makes no sense. 

That is a nice alternate explanation Chris.  

It is more technical than mine which is a good thing, maybe it will help people understand the notation.   

No that is not correct.

Average rate of change from x=5 to x=9 is

\(\frac{f(9)-f(5)}{9-5}   \)

What is f(9) ?      What is f(5) ?    Look at the table. 

No one answer over the top of me please.  I'm trying to teach.

I will give you a very big hint:

the denominator is of the from    x^2+x+1 where   x=cube root of 3

AND

(x-1)( x^2+x+1) = x^3-1

You need to rationalize the denominator.

Please no one answer over the top of me - I am trying to help guest learn!

Try using x = 0,1,2,3 etc   and see what f(x)  and g(x) are 

see when they give the same answer :)