Answer
Domain: $[-2, 6]$
Range: $[-6, 18]$
Work Step by Step
The given function $f(x)=3x$ has its domain restricted to $-2 \le x \le 6$.
Thus, its domain is $[-2, 6]$.
The function $f(x)=3x$ is linear with a positive slope. This means that as the value of $x$ increases, the value of $y$, also increases.
Thus, within its domain, the function's minimum value is at $x=-2$, and its maximum value will be at $x=6$.
Find the value of $y$ when $x=-2$ and when $x=6$ to have:
When x = -2,
$f(-2)=3(-2) = -6$
When x = 6,
$f(6) = 3(6) = 18$
This means that the y-values of the function range from -6 to 18.
Therefore the range of the function is $[-6, 18]$
