Understanding Domain and Range

The video tutorial explains the concept of domain in functions, focusing on the function g(y) = √(y-6). It discusses the properties of square roots, emphasizing that the input must be zero or positive to yield a real number. The tutorial demonstrates how to determine the domain by solving inequalities. Additionally, it introduces piecewise functions, explaining how their domain is defined by specific input values.

What is the domain of a function?

• The set of all possible inputs

• The set of all possible outputs

• The set of all possible equations

• The set of all possible graphs

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

• It results in a real number

• It results in a positive number

• It results in a complex number

• It results in a zero

What must be true for the inside of a square root to ensure a real output?

• It must be less than zero

• It must be equal to zero

• It must be a negative number

• It must be greater than or equal to zero

What is the domain of the function g(y) = √(y-6)?

• y < 6

• y ≥ 6

• y > 6

• y ≤ 6

What happens if you plug in a value less than 6 into g(y) = √(y-6)?

• You get an error

• You get a real number

• You get a negative number

• You get a positive number

What symbol is used to indicate that a value is included in the domain?

• Greater than

• Less than

• Greater than or equal to

• Less than or equal to

In a piecewise function, what determines the domain?

• The graph of the function

• The specific values given

• The general equation

• The range of the function

If a piecewise function specifies x = pi and x = 3, what is the domain?

• Only pi and 3

• All real numbers

• Only numbers greater than 3

• Only numbers less than pi

What is the range of the piecewise function given in the example?

• Only positive numbers

• pi and 3

• All real numbers

• 1 and 0

What will be discussed in the next video?

• Square roots

• Domain

• Range

• Piecewise functions