Gradient Function Investigation

1461 Words3 Pages

Gradient Function Investigation

Gradient Function

In this investigation I am going to investigate the gradients of the

graphs Y=AXN Where A and N are constants. I shall then use the

information to find a formula for all curved graphs.

To start the investigation I will draw the graphs where A=1 and N= a

positive integer.

Y=X2

X

Height

Width

Gradient

1

1

0.5

2

2

4

1

4

3

9

1.5

6

4

16

2

8

Looking at the results above I can see that the gradient is twice the

X value, the height is X2 and the width is 1/2 the X value. This shows

me that there are several patterns in the graph but there is not

enough to make a formula on so I am going to do another graph

Y=X3

X

Height

Width

Gradient

1

1

0.33

3

2

8

0.66

12

3

27

1

27

4

64

1.33

48

There are some more patterns in this table, the height is now X3 and

the width is 1/3 of the X value. I can see no pattern between the

Gradient and the X value in this table.

By comparing the two tables I can see that the height is what Y equals

(AXN) and the width is the 1 over the power (X/2 for X2 and X/3 for X3).

So if the formula for the gradient is Height/Width then, by replacing

the height with AXN and the width with X/N we get XN/(X/N). We can

simplify this by multiplying both sides by N to get ANXN/X and we can

simplify this by dividing both sides by X to get ANXN-1.

I shall now you this formula in the graph Y=X4 to test it.

Open Document