Domain of a radical with negative under the radical

The video tutorial explains how to determine the domain of a function involving a radical expression. It begins by discussing the necessity for the expression under the radical to be non-negative. The tutorial then demonstrates solving inequalities to find the domain, emphasizing the importance of flipping the inequality sign when multiplying or dividing by a negative number. Finally, it covers converting inequalities into interval notation, providing tips for those who may find the process challenging.

What must be true about the expression under a radical for the function to be defined?

• It must be greater than zero.

• It must be equal to zero.

• It must be less than zero.

• It must be greater than or equal to zero.

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

• Add the negative number to both sides.

• Flip the inequality sign.

• Subtract the negative number from both sides.

• Keep the inequality sign the same.

Which of the following is the correct interval notation for the inequality x ≤ 2?

• (-∞, 2]

• [2, ∞)

• (-∞, 2)

• [2, ∞]

What is a helpful tool to use when struggling with interval notation?

• Graphing the inequality.

• Using a calculator.

• Drawing the inequality.

• Memorizing the rules.

Why might it be beneficial to write inequalities before converting to interval notation?

• It saves time.

• It helps visualize the solution.

• It makes the problem more complex.

• It is required by all math teachers.