Question

What are the domain and range of the algebraic function you found by graphing the equation y = 36 – 3x? Please hurry I'm being timed and I don't understand this!!!!

Answer 1

Domain
`=(-\infty,\ \infty)`

Range
`=(-\infty,\ \infty)`

Explanation:

Domain : Domain of a function
`f(x)` is the set of all possible values of
`x` for which
`f(x)` exists.

Range : range of a function
`f(x)` is the set of all possible values of
`f(x)`.

Here
`f(x)=36-3x`

`x` can be any value from
`-\infty` to
`\infty`.

`\forall\ x=a\ there\ exists\ f(x)\ such\ that\ f(a)=36-3a`

hence possible value of
`x` can be any value between
`-\infty` and
`\infty`

`domain =(-\infty,\ \infty)`

let
`y=-f(x)`

`y=36-3x\\3x=36-y\\\\\\x=(36-y)/(3)\\`

so
`\forall\ f(x)=y\ there\ exist\ x\ \in(-\infty,\ \infty)`.

hence
`f(x)` can have any value between
`-\infty\ to\ \infty.`.

Range
`=(-\infty,\ \infty)`