Understanding Domain and Square Roots

The video tutorial explains the concept of domain in functions, using a function named g(x) as an example. It introduces the idea of domain as the set of all possible inputs and contrasts it with the range, which is the set of possible outputs. The tutorial focuses on functions involving square roots, emphasizing that the expression inside a square root must be zero or positive to be defined. The instructor demonstrates how to determine the domain of a function with a square root by ensuring the expression inside is non-negative, using inequalities to express the domain. The example used is the function x minus six under a square root, where x must be six or greater.

What is the domain of a function generally concerned with?

• The name of the function

• The possible inputs for the function

• The outputs of the function

• The letters used in the function

What is the range of a function?

• The letters used in the function

• The name of the function

• The outputs of the function

• The inputs of the function

Why can't negative numbers be inside a square root?

• They are not integers

• They are too small

• They are too large

• They result in undefined values

What happens if you input zero into the square root function discussed?

• You get zero

• You get a positive number

• You get an undefined value

• You get a negative number

For the function x minus six under a square root, what is the smallest value x can be?

• 5

• 6

• 7

• 8

What does the inequality symbol in the domain expression indicate?

• x must be less than a number

• x must be equal to a number

• x must be greater than or equal to a number

• x must be not equal to a number

What is the domain of the function x minus six under a square root?

• x < 6

• x ≤ 6

• x > 6

• x ≥ 6

What is the result when x equals six in the function x minus six under a square root?

• Undefined

• Zero

• A negative number

• A positive number

What is the significance of the number six in the function x minus six under a square root?

• It is the value that makes the square root undefined

• It is the value that makes the square root zero

• It is the minimum value for x

• It is the maximum value for x

What does the domain of a function ensure in terms of the square root?

• The inside of the square root is undefined

• The inside of the square root is zero or positive

• The inside of the square root is positive

• The inside of the square root is negative