Domain and Continuity of Functions

The video tutorial explains how to find the domain of four different functions. It begins by outlining two key points: the denominator of a function should never be zero, and the term inside a square root should always be positive. The tutorial then walks through the process of finding the domain for each function, using number lines and solving inequalities to determine which values are included or excluded from the domain. The video covers functions with simple denominators, quadratic expressions, and square roots, providing a comprehensive guide to understanding function domains.

What are the two key rules to remember when finding the domain of a function?

• The denominator must not be zero, and the term inside a square root must be positive.

• The numerator must always be zero, and the denominator must be positive.

• The numerator must be positive, and the denominator must be zero.

• The function must be continuous, and the term inside a square root must be negative.

For the function f(x) = 1/(x-2), which value is excluded from the domain?

• x = 2

• x = 0

• x = 3

• x = 1

What is the domain of the function f(x) = 1/(x-2)?

• (-∞, ∞)

• (-∞, 2]

• [2, ∞)

• (-∞, 2) ∪ (2, ∞)

For the function 1/(x^2 - x - 6), which values are excluded from the domain?

• x = -3 and x = 2

• x = -2 and x = 3

• x = 1 and x = 4

• x = 0 and x = 1

What is the domain of the function 1/(x^2 - x - 6)?

• (-∞, -2) ∪ (3, ∞)

• (-∞, ∞)

• (-∞, -2) ∪ (-2, 3) ∪ (3, ∞)

• (-∞, 3) ∪ (3, ∞)

In a function with a square root in the numerator, what must be true about the term inside the square root?

• It must be greater than or equal to zero.

• It must be greater than zero.

• It must be less than zero.

• It must be equal to zero.

For a function with a square root in the numerator, what is the domain if the term inside the square root is x - 1?

• (-∞, ∞)

• (-∞, 1]

• [1, ∞)

• (1, ∞)

In a function with a square root in the denominator, what must be true about the expression?

• It must be greater than zero.

• It must be less than zero.

• It must be greater than or equal to zero.

• It must be equal to zero.

What is the domain of a function where the expression x^2 - 4 is in the denominator?

• (-∞, -2] ∪ [2, ∞)

• (-∞, 2) ∪ (2, ∞)

• (-∞, -2) ∪ (2, ∞)

• (-∞, ∞)

Why can't we write 'greater than or equal to zero' for the expression in the denominator?

• It would make the function undefined.

• It would make the function continuous.

• It would make the function positive.

• It would make the function zero.