Write the domain of a rational function with radicals

The video tutorial discusses solving algebra problems with constraints, focusing on radicals and denominators. It explains how to handle inequalities, including flipping signs when dividing by negatives. The tutorial also covers domain restrictions, emphasizing that imaginary numbers are not part of the domain. Finally, it concludes with a discussion on the domain of real numbers and included values.

What is the first constraint to consider when dealing with a radical in an algebraic expression?

• The expression under the radical must be negative.

• The expression under the radical must be zero.

• The expression under the radical must be positive.

• The expression under the radical must be non-negative.

When solving inequalities, what must you remember to do when dividing by a negative number?

• Multiply both sides by a positive number.

• Flip the inequality sign.

• Add a constant to both sides.

• Keep the inequality sign the same.

What happens to the domain of a function when the expression under a radical is negative?

• The domain includes imaginary numbers.

• The domain includes all real numbers.

• The domain remains unchanged.

• The domain excludes imaginary numbers.

Which of the following is NOT a valid domain restriction for a function with a denominator?

• The denominator must be non-zero.

• The denominator can be zero.

• The denominator must be negative.

• The denominator must be positive.

What is the valid domain for the function discussed in the video?

• All real numbers less than or equal to 1.

• All real numbers except those that make the expression under the radical negative.

• All real numbers greater than or equal to 1.

• All real numbers except those that make the denominator zero.