Question

Which option below correctly describes the domain of (see image) and explains why the range of b is not all real numbers?

a. The domain is all real numbers less than or equal to 81.

The range is not all real numbers because the square root of a negative number is not a real number.

b. The domain is all real numbers less than or equal to 81.

The range is not all real numbers because the square root symbol applied to a non-negative number is non-negative.

c. The domain is all real numbers greater than or equal to 81.

The range is not all real numbers because the square root of a negative number is not a real number.

d. The domain is all real numbers greater than or equal to 81.

The range is not all real numbers because the square root symbol applied to a non-negative number is non-negative.

Answer 1

b. The domain is all real numbers less than or equal to 81; and The range is not all real numbers because the square root symbol applied to a non-negative number is non-negative.

Explanation:

The square root function is not defined in the real number system for the square root of a negative number.

In order for the number under the radical sign to be positive, then the value of x must be all numbers less than or equal to 81.

The range cannot be negative numbers, since the square root of a positive number will give a positive answer.

This makes the correct choice b.

Answer 2

The domain is all real numbers less than or equal to 81.

The range is not all real numbers because the square root symbol applied to a non-negative number is non-negative