Question

How do you write a function rule for `x = 2, 4, 6` and `y = 1, 0, -1`?

Answer 1

`y=f(x) = -1/2x+2`

Explanation:

Set the `i^("th")` point as: `P_i->(x_i,y_i)`

Change in `x` sequence is `2`
Change in `y` sequence is `-1`

Gradient (slope) `->m=("change in "y)/("change in " x) =-1/2`

Assuming there is a direct link between `x and y` numbers of sequence we have:

`P_1->(x_1,y_1)=(2,1)`
`P_2->(x_2,y_2)=(4,0)`
`P_3->(x_3,y_3)->(6 ,-1 )`

Relating `m` to, say, point 2 we have:

`m=-1/2=(y-y_2)/(x-x_2)=(y-0)/(x-4)`

`-1/2= (y-0)/(x-4)`

Multiply both sides by `(+2)`

`-1=(2(y-0))/(x-4)`

Multiply both sides by `(x-4)`

`-(x-4)=2y`

`-x+4=2y`

`y=-1/2x+2`
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The question is specific in that it states 'function rule for `x`'

So we write it as: `y=f(x) = -1/2x+2`