Question

For a function f(x) =-4-2x, the domain is {-3,-2,-1,0,1,}. What is the range of the function?

Answer 1

$\boxed{\{2,0,-2,-4,-6\}}$

Explanation:

Recall the concept of functions that states:

A function $f$ from a set $A$ to a set $B$ is a relation that assigns to each element $x$ in the set $A$ exactly one element $y$ in the set $B$. The set $A$ is the domain (also called the set of inputs) of the function and the set $B$ contains the range (also called the set of outputs).

In this case, we have a se $A$ given by:

$\{-3,-2,-1,0,1\}$

So we need to find the range or set of outputs. We have the function given by the following equation:

$f(x) =-4-2x \\ \\ Where: \\ \\ The \ set \ of \ all \ x-values \ for \ which \ the \\ function \ is \ valid \ is \ the \ domain \\ \\ \\ The \ set \ of \ all \ y-values \ for \ which \ the \\ function \ is \ valid \ is \ the \ range$

Therefore, our goal is to find the set of all y-values for which the function is defined:

$\bullet \ For \ x=-3: \\ \\ y=-4-2(-3) \\ \\ y=-4+6 \\ \\ y=2$

$\bullet \ For \ x=-2: \\ \\ y=-4-2(-2) \\ \\ y=-4+4 \\ \\ y=0$

$\bullet \ For \ x=-1: \\ \\ y=-4-2(-1) \\ \\ y=-4+2 \\ \\ y=-2$

$\bullet \ For \ x=0: \\ \\ y=-4-2(0) \\ \\ y=-4 \\ \\ y=-4$

$\bullet \ For \ x=1: \\ \\ y=-4-2(1) \\ \\ y=-4-2 \\ \\ y=-6$

Finally, the range of the function is the set $B$:

$\boxed{\{2,0,-2,-4,-6\}}$

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