To find the domain,
Domain is [0, ∞)
To find the range evaluate the function using the domain.
y = 2√0 = 0
y = 2√1 = 2
y = 2√4 = 4
This continues forever.
Range is [0, ∞).
In an odd root, the domain is all real numbers. That is because raising a negative number to an odd power is negative, and raising a positive number to an odd power is positive. It has not restrictions. Knowing that, what is the range of the function? Well, lets pick a large negative number and large positive number as x. We will use these values of x to evaluate y. We should also evaluate when x=0. At this value of x, y=0.
y = -3 * 3√(-216) = -3 * -6 = 18
y = -3 * 3√(216) = -3 * 6 = -18
If we decrease x from -216 and increase x from 216, y will increase from 18 and y will decrease from -18. Do you see the pattern.
The range is all real numbers (-∞, ∞).
Note that problem 4 has the same situation here.
Try problems 3 and 4 on your own using the same procedure.