Understanding the Domain of a Square Root Function

The video tutorial explains how to determine the domain of the function f(x) = √(y² - x²). It discusses the necessity for the radicand to be non-negative, leading to the inequality y² - x² ≥ 0. The tutorial demonstrates factoring the expression as a difference of squares and solving the inequality by considering cases where the product is zero, positive, or negative. It then shows how to graph the lines y = x and y = -x, and identify regions A and C as part of the domain. The video concludes by verifying the domain using a graph of the function.

What must be true about the expression under the square root for the function to be real?

• It must be zero.

• It must be positive.

• It must be non-negative.

• It must be negative.

What is the result of factoring the expression y^2 - x^2?

• (y + x)(y + x)

• (y - x)(y - x)

• (y + x)(y - x)

• (y - x)(y + x)

Which lines are included in the domain of the function?

• y = x and y = -x

• y = x and y = y

• y = -x and y = 0

• y = x and y = 0

What is the slope of the line y = -x?

• 2

• 0

• -1

• 1

What is the vertical intercept of the line y = x?

• 2

• -1

• 0

• 1

In which region do both inequalities y > x and y > -x hold true?

• Region D

• Region C

• Region B

• Region A

What is the result of solving the inequality y < x?

• Shade below the line y = x

• Shade below the line y = -x

• Shade above the line y = x

• Shade above the line y = -x

Which regions are part of the domain of the function?

• Regions C and D

• Regions A and B

• Regions A and C

• Regions B and C

What does the graph of the function resemble?

• A cylinder

• A sphere

• A double cone

• A single cone

What is the significance of the lines y = x and y = -x in the context of the domain?

• They are boundaries of the domain.

• They are included in the domain.

• They are excluded from the domain.

• They are irrelevant to the domain.