Question

79 points to the person who answers the whole page:
Here is first page to answer these questions

2)for each function, write an expression for the xth term

W(x)=
G(x)=
T(x)=

3) graph all three function on the coordinate plane to the right.

4) which function(s) has a faster rate of change?___
Where do you see this pattern, in the table and in the graph?

Pattern:__________________________________


Table:____________________________________


Graph:___________________________________

Answer 1

Answer:

This has no single answer. You are going to have to read through it.

Step-by-step explanation:

Part 2

W(x) = 1 It's a constant. There is always at least 1 white term for n = 1,2,3 ...

G(x) = n^2 - 1                  The 1 represents the white square.

T(x) = G(x) + W(x) = n^2 - 1 + 1 = n^2

Part 3

The graphs are given below. You can translate it onto the graph you are given.

Part 4

W(n) has no rate of change at all. You can see it in the table. All the answers values for W(n) = 1 no matter what n is

G(n) has a rate of change of (n^2 - 1) - (n -1)^2 - 1 which when the brackets are removed and the subtraction done, the rate of change

= n2 - 1  - [(n - 1)^1 - 1]

= n^2 - 1 - ((n^2 - 2n + 1) - 1)

= n^2 - 1 - n^2 + 2n - 1 + 1

= 2n - 1 where n is the number of gray squares on one side.

So for n = 4  (which is 4 gray squares on 1 side)

The rate of change is 2*4 - 1 between the n = 3 and n =4

The graph shows the steeper graph is T(n)

The fastest rate of change is T(n). It includes white and gray.