find the domain and range of y=f(x)

Question

{4 if -6</= x< -2
f(x)={absolute value of x if -2</= x< 8
{cubed root of x if 8</= x</= 14

it is piecewise, I am completely lost on how to even set up this function.

Answer 1

the domain is all the values of x where f(x) is defined.

f(x) =
4 if -6 <= x < -2
|x| if -2 <= x < 8
∛x if 8 <= x <= 14

So, clearly the domain is [-8,14] since f(x) is defined everywhere inside the interval, and nowhere outside it.

Doesn't matter how piecewise it is. You just care about how it is defined. Just be sure to check that the pieces join up at the ends, leave no holes, and don't overlap.