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

Answer:

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

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

Step-by-step 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 $y=-f(x)$

$y=36-3x\\3x=36-y\\\\\\x=\frac{36-y}{3}$

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

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

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