Michael J. answered • 02/05/17

Tutor

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Great at Simplifying Complex Concepts and Processes

1)

To find the domain,

set x≥0.

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, ∞).

2)

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 = 18y = -3 *

^{3}√(216) = -3 * 6 = -18If 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.