Question

---- PLEASE HELP <3 .. with steps :( <3

#1.)

Find the first 3 iterations of the function here: g(x)3x if you have an initial value of 2.

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#2.)

Find the first iterations of the function here: g(x)=1/3x+1 if you have an initial value of 2.

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#3.)

Find the first 3 iterations of the function here: g(x)-1|x-2|+3 if you have an initial value of 0.5

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THANK YOU <3

Answer 1

1) 6, 18, 54

2) 5/3, 14/9, 41/27

3) 1.5, 2.5, 2.5

Explanation:

1)

The function that we have in this problem is

`g(x)=3x`

We want to find the first 3 iterations.

The initial value is:

x = 2

To find the value of the 1st iteration, we just substitute this value into the expression of the function, and we get:

`g_1(x)=3x=3\cdot 2 = 6`

The to find the value of the 2nd iteration, we just substitute this value into the expression of the function, and we get:

`g_2(x)=3\cdot g_1(x)=3\cdot 6 = 18`

Finally, the 3rd iteraction is given by:

`g_3(x)=3g_2(x)=3\cdot 18=54`

2)

Here in this problem the function that we have to use is

`g(x)=(1)/(3)x+1`

The initial value is

`x=2`

So the first iteration is given by

`g_1(x)=(1)/(3)\cdot 2 + 1 = (5)/(3)`

To find the 2nd iteration, we substitute this value into g(x) again:

`g_2(x)=(1)/(3)g_1+1=(1)/(3)\cdot (5)/(3)+1=(5)/(9)+1=(14)/(9)`

Finally, to find the 3rd iteration, we substitute this value into g(x) again:

`g_3(x)=(1)/(3)\cdot (14)/(9)+1=(14)/(27)+1=(41)/(27)`

3)

The function in this problem is

`g(x)=-|x-2|+3`

The initial value is

x = 0.5

So, the first iteration is:

`g_1(x)=-1|0.5-2|+3=-1|-1.5|+3=-1\cdot 1.5 +3=-1.5+3=1.5`

The second iteration is given by

`g_2(x)=-|g_1-2|+3=-|1.5-2|+3=--0.5+3=2.5`

Finally, the 3rd iteration is

`g_3(x)=-|g_2-2|+3=-|2.5-2|+3=-0.5+3=2.5`