OK, I see the worksheet itself is a little hard to understand the way it's written, but I'll try to answer:

a)

is a function for all real x. This could be written in several different ways, including

and

.

b)

Greater than zero:

Less than zero:

Equal to zero:

c) The domain of

is

. This corresponds to

.

Follow up question:

is a function for

because all real numbers have exactly one real cube root. Thus as long as

is a real number,

will associate it with a unique value. The range is also all real numbers.

Integrative Activity: For a function

, the domain of

is described by

.